subject:(A priori estimates)

University of New South Wales

1. Shafie, Sabarina. Mixed finite element methods for nonlinear equations: a priori and a posteriori error estimates.

Degree: Mathematics & Statistics, 2016, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/56899 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41912/SOURCE02?view=true

► A priori error estimation provides informationabout the asymptotic behaviorof the approximate solution andinformationon convergence rates of the problem. Contrarily,a posteriori error estimation derives the estimation… (more)

▼ A priori error estimation provides informationabout the asymptotic behaviorof the approximate solution andinformationon convergence rates of the problem. Contrarily,a posteriori error estimation derives the estimation of the exact errorby employing the approximate solution and providesa practical accurate error estimation.Additionally, a posteriori error estimates can be used to steer adaptive schemes,that is to decide the refinement processes,namely local mesh refinement orlocal order refinement schemes. Adaptive schemes offinite element methods for numerical solutions of partial differential equationsare considered standard toolsin science and engineering to achieve better accuracywith minimum degrees of freedom.In this thesis, we focus on a posteriori error estimationsof mixed finite element methods for nonlineartime dependent partial differential equations.Mixed finite element methods are methods which are based on mixedformulations of the problem. In a mixed formulation,the derivative of the solution is introduced as aseparate dependent variable in a different finite element space than the solution itself.We implement the H¹-Galerkin mixed finite element method (H1MFEM)to approximate the solution and its derivative.Two nonlinear time dependent partial differential equations are considered in this thesis,namely the Benjamin-Bona-Mahony (BBM) equation and Burgers equation.Our a posteriori error estimations are based on implicit schemes of a posteriori errorestimations, where the error estimators are locally computed on each element.We propose a posteriori error estimates by using the approximate solution produced by H1MFEMand use the a posteriori error estimates to compute the local error estimators,respectively for the BBM and Burgers equations.Then, we prove that the introduced a posteriori error estimates are accurate and efficient estimations of the exact errors.The last part of this study is on numerical studies of adaptive meshrefinement schemes for the two equations mentioned above.By implementing the introduced a posteriori error estimates,we propose adaptive mesh refinement schemes of H1MFEM for both equations. Advisors/Committee Members: Tran, Thanh, Mathematics & Statistics, Faculty of Science, UNSW.

Subjects/Keywords: Finite element methods; A posteriori error estimates; A priori error estimates; BBM equation; Burgers equation

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APA (6^th Edition):

Shafie, S. (2016). Mixed finite element methods for nonlinear equations: a priori and a posteriori error estimates. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/56899 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41912/SOURCE02?view=true

Chicago Manual of Style (16^th Edition):

Shafie, Sabarina. “Mixed finite element methods for nonlinear equations: a priori and a posteriori error estimates.” 2016. Doctoral Dissertation, University of New South Wales. Accessed April 12, 2021. http://handle.unsw.edu.au/1959.4/56899 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41912/SOURCE02?view=true.

MLA Handbook (7^th Edition):

Shafie, Sabarina. “Mixed finite element methods for nonlinear equations: a priori and a posteriori error estimates.” 2016. Web. 12 Apr 2021.

Vancouver:

Shafie S. Mixed finite element methods for nonlinear equations: a priori and a posteriori error estimates. [Internet] [Doctoral dissertation]. University of New South Wales; 2016. [cited 2021 Apr 12]. Available from: http://handle.unsw.edu.au/1959.4/56899 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41912/SOURCE02?view=true.

Council of Science Editors:

Shafie S. Mixed finite element methods for nonlinear equations: a priori and a posteriori error estimates. [Doctoral Dissertation]. University of New South Wales; 2016. Available from: http://handle.unsw.edu.au/1959.4/56899 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:41912/SOURCE02?view=true

Universidade Estadual de Campinas

2. Vieira, Rafael Albiero, 1995-. Indexicalidade nos casos do contingente a priori.

Degree: Instituto de Filosofia e Ciências Humanas; Programa de Pós-Graduação em Filosofia, 2019, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/335804

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Orientador: Marco Antonio Caron Ruffino

Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas

Made available in DSpace on 2020-01-16T19:42:12Z (GMT).… (more)

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Orientador: Marco Antonio Caron Ruffino

Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas

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Resumo: O fenômeno do contingente a priori surgiu com Kripke, quando ele chamou atenção para o fato de que somos capazes de conhecer, em casos específicos, sentenças contingentes de maneira a priori. Após esta ideia ter sido incorporada na tradição, alguns filósofos perceberam uma grande relação entre os exemplos kripkeanos e os termos indexicais. Gareth Evans, por exemplo, afirmou que tal relação nos revelaria que os casos kripkeanos não passariam de sentenças superficiais e, portanto, não problemáticas. Entretanto, uma consequência da teoria de Evans é a de que grande parte do nosso conhecimento que envolve indexicais se torna trivial. Dentro deste debate, o objetivo deste texto é explorar o contingente a priori, as categorias de contingência propostas por Evans, e as principais consequências deste debate

The contingent a priori phenomenon emerged with Kripke, when he pointed out that we are able to know, in specific cases, contingent a priori sentences. After this idea was incorporated into the tradition, some philosophers perceived a great relation between the kripkean examples and the indexical terms. Gareth Evans, for example, argued that such a relation would reveal that kripkean cases would be only superficial and thus not problematic. However, a consequence of Evans¿ theory is that much of our knowledge involving indexicals becomes trivial. Within this debate, the purpose of this text is to explore the contingent a priori, the contingency categories by Evans, and the main consequences of this debate

Mestrado

Filosofia

Mestre em Filosofia

2016/25914-3

FAPESP

CAPES

Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS, Ruffino, Marco Antonio Caron, 1963-, Boccardi, Emiliano, Merlussi, Pedro.

Subjects/Keywords: Kripke, Saul A., 1940-; Filosofia; Epistemologia; Estimativas a-priori; Kripke, Saul Aaron; A priori estimates; Epistemology; Philosophy

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APA (6^th Edition):

Vieira, Rafael Albiero, 1. (2019). Indexicalidade nos casos do contingente a priori. (Masters Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/335804

Chicago Manual of Style (16^th Edition):

Vieira, Rafael Albiero, 1995-. “Indexicalidade nos casos do contingente a priori.” 2019. Masters Thesis, Universidade Estadual de Campinas. Accessed April 12, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/335804.

MLA Handbook (7^th Edition):

Vieira, Rafael Albiero, 1995-. “Indexicalidade nos casos do contingente a priori.” 2019. Web. 12 Apr 2021.

Vancouver:

Vieira, Rafael Albiero 1. Indexicalidade nos casos do contingente a priori. [Internet] [Masters thesis]. Universidade Estadual de Campinas; 2019. [cited 2021 Apr 12]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/335804.

Council of Science Editors:

Vieira, Rafael Albiero 1. Indexicalidade nos casos do contingente a priori. [Masters Thesis]. Universidade Estadual de Campinas; 2019. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/335804

University of Bath

3. Millward, Raymond. A new adaptive multiscale finite element method with applications to high contrast interface problems.

Degree: PhD, 2011, University of Bath

URL: https://researchportal.bath.ac.uk/en/studentthesis/a-new-adaptive-multiscale-finite-element-method-with-applications-to-high-contrast-interface-problems(bb401e2e-2eeb-49bb-a652-0af58499481c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.544505

► In this thesis we show that the finite element error for the high contrast elliptic interface problem is independent of the contrast in the material… (more)

▼ In this thesis we show that the finite element error for the high contrast elliptic interface problem is independent of the contrast in the material coefficient under certain assumptions. The error estimate is proved using a particularly technical proof with construction of a specific function from the finite dimensional space of piecewise linear functions. We review the multiscale finite element method of Chu, Graham and Hou to give clearer insight. We present some generalisations to extend their work on a priori contrast independent local boundary conditions, which are then used to find multiscale basis functions by solving a set of local problems. We make use of their regularity result to prove a new relative error estimate for both the standard finte element method and the multiscale finite element method that is completely coefficient independent. The analytical results we explore in this thesis require a complicated construction. To avoid this we present an adaptive multiscale finite element method as an enhancement to the adaptive local-global method of Durlofsky, Efendiev and Ginting. We show numerically that this adaptive method converges optimally as if the coefficient were smooth even in the presence of singularities as well as in the case of a realisation of a random field. The novel application of this thesis is where the adaptive multiscale finite element method has been applied to the linear elasticity problem arising from the structural optimisation process in mechanical engineering. We show that a much smoother sensitivity profile is achieved along the edges of a structure with the adaptive method and no additional heuristic smoothing techniques are needed. We finally show that the new adaptive method can be efficiently implemented in parallel and the processing time scales well as the number of processors increases. The biggest advantage of the multiscale method is that the basis functions can be repeatedly used for additional problems with the same high contrast material coefficient.

Subjects/Keywords: 518; structural optimisation; parallel; finite element; adaptive; random fields; iterative; multiscale; regularity; a priori estimates

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APA (6^th Edition):

Millward, R. (2011). A new adaptive multiscale finite element method with applications to high contrast interface problems. (Doctoral Dissertation). University of Bath. Retrieved from https://researchportal.bath.ac.uk/en/studentthesis/a-new-adaptive-multiscale-finite-element-method-with-applications-to-high-contrast-interface-problems(bb401e2e-2eeb-49bb-a652-0af58499481c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.544505

Chicago Manual of Style (16^th Edition):

Millward, Raymond. “A new adaptive multiscale finite element method with applications to high contrast interface problems.” 2011. Doctoral Dissertation, University of Bath. Accessed April 12, 2021. https://researchportal.bath.ac.uk/en/studentthesis/a-new-adaptive-multiscale-finite-element-method-with-applications-to-high-contrast-interface-problems(bb401e2e-2eeb-49bb-a652-0af58499481c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.544505.

MLA Handbook (7^th Edition):

Millward, Raymond. “A new adaptive multiscale finite element method with applications to high contrast interface problems.” 2011. Web. 12 Apr 2021.

Vancouver:

Millward R. A new adaptive multiscale finite element method with applications to high contrast interface problems. [Internet] [Doctoral dissertation]. University of Bath; 2011. [cited 2021 Apr 12]. Available from: https://researchportal.bath.ac.uk/en/studentthesis/a-new-adaptive-multiscale-finite-element-method-with-applications-to-high-contrast-interface-problems(bb401e2e-2eeb-49bb-a652-0af58499481c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.544505.

Council of Science Editors:

Millward R. A new adaptive multiscale finite element method with applications to high contrast interface problems. [Doctoral Dissertation]. University of Bath; 2011. Available from: https://researchportal.bath.ac.uk/en/studentthesis/a-new-adaptive-multiscale-finite-element-method-with-applications-to-high-contrast-interface-problems(bb401e2e-2eeb-49bb-a652-0af58499481c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.544505

West Virginia University

4. Lagha, Aesha. Global existence and Asymptotic Behavior of the Solutions to Models for Chemotaxis Systems with Chemo Attractants and Repellents.

Degree: PhD, Mathematics, 2020, West Virginia University

URL: https://doi.org/10.33915/etd.7965 ; https://researchrepository.wvu.edu/etd/7965

► We study global existence and asymptotic behavior of the solutions to models for chemotaxis systems with chemo attractants and repellents in three dimensions. Chemo… (more)

Subjects/Keywords: energy method; a priori estimates; Fourier transform; time-decay rate; Partial Differential Equations

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APA (6^th Edition):

Lagha, A. (2020). Global existence and Asymptotic Behavior of the Solutions to Models for Chemotaxis Systems with Chemo Attractants and Repellents. (Doctoral Dissertation). West Virginia University. Retrieved from https://doi.org/10.33915/etd.7965 ; https://researchrepository.wvu.edu/etd/7965

Chicago Manual of Style (16^th Edition):

Lagha, Aesha. “Global existence and Asymptotic Behavior of the Solutions to Models for Chemotaxis Systems with Chemo Attractants and Repellents.” 2020. Doctoral Dissertation, West Virginia University. Accessed April 12, 2021. https://doi.org/10.33915/etd.7965 ; https://researchrepository.wvu.edu/etd/7965.

MLA Handbook (7^th Edition):

Lagha, Aesha. “Global existence and Asymptotic Behavior of the Solutions to Models for Chemotaxis Systems with Chemo Attractants and Repellents.” 2020. Web. 12 Apr 2021.

Vancouver:

Lagha A. Global existence and Asymptotic Behavior of the Solutions to Models for Chemotaxis Systems with Chemo Attractants and Repellents. [Internet] [Doctoral dissertation]. West Virginia University; 2020. [cited 2021 Apr 12]. Available from: https://doi.org/10.33915/etd.7965 ; https://researchrepository.wvu.edu/etd/7965.

Council of Science Editors:

Lagha A. Global existence and Asymptotic Behavior of the Solutions to Models for Chemotaxis Systems with Chemo Attractants and Repellents. [Doctoral Dissertation]. West Virginia University; 2020. Available from: https://doi.org/10.33915/etd.7965 ; https://researchrepository.wvu.edu/etd/7965

University of Texas – Austin

5. -3958-8871. A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2018, University of Texas – Austin

URL: http://hdl.handle.net/2152/68968

► Multiscale modeling of subsurface flow and transport is a major area of interest in several applications including petroleum recovery evaluations, nuclear waste disposal systems, CO₂… (more)

▼ Multiscale modeling of subsurface flow and transport is a major area of interest in several applications including petroleum recovery evaluations, nuclear waste disposal systems, CO₂ sequestration, groundwater remediation and contaminant plume migration in heterogeneous porous media. During these processes the direct numerical simulation is computationally intensive due to detailed fine scale characterization of the subsurface formations. The main objective of this work is to develop an efficient multiscale framework to reduce usage of fine scale properties associated with advection and diffusion/dispersion, while maintaining accuracy of quantities of interest including mass balance, pressure, velocity, concentration. Another purpose of this work is to investigate the adaptivity criteria in transport and flow problems numerically and/or theoretically based on error estimates. We propose a new adaptive numerical homogenization method using numerical homogenization and Enhanced Velocity Mixed Finite Element Method (EVMFEM). We focus on upscaling the permeability and porosity fields for slightly (nonlinear) compressible single phase Darcy flow and transport problems in heterogeneous porous media. The fine grids are used in the transient regions where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [85]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this dissertation, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium. We have also derived a priori error estimate for a parabolic problem using Backward Euler and Crank-Nicolson method in time and EVMFEM in space. Next, we have established a posteriori error estimate in EVMFEM setting for incompressible flow problems. We first propose the flux reconstruction for error estimates and prove the upper and lower bound theorems. Next, the explicit residual-based estimates and the recovery-based error estimates with the post-processed pressure are derived theoretically. Numerical experiments are conducted to show that the proposed estimators are effective indicators of local error for incompressible flow problems. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Arbogast, Todd (committee member), Balhoff, Matthew (committee member), Tsai, Yen-Hsi Richard (committee member), Wildey, Tim (committee member).

Subjects/Keywords: Enhanced velocity; Numerical homogenization; Adaptive mesh refinement; Multiscale methods; Error estimates; A posteriori error; A priori error; SPE10 dataset

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APA (6^th Edition):

-3958-8871. (2018). A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68968

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-3958-8871. “A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed April 12, 2021. http://hdl.handle.net/2152/68968.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-3958-8871. “A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme.” 2018. Web. 12 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-3958-8871. A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2152/68968.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-3958-8871. A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/68968

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Pontifical Catholic University of Rio de Janeiro

6. GABRIELLE SALLER NORNBERG. [en] METHODS OF THE REGULARITY THEORY IN THE STUDY OF PARTIAL DIFFERENTIAL EQUATIONS WITH NATURAL GROWTH IN THE GRADIENT.

Degree: 2019, Pontifical Catholic University of Rio de Janeiro

URL: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36015

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[pt] Nesta tese de Doutorado estudamos uma classe de equações diferenciais parciais de segunda ordem, uniformemente elípticas, completamente não-lineares na forma não-divergência, com crescimento superlinear… (more)

Subjects/Keywords: [pt] EXISTENCIA; [en] EXISTENCE; [pt] VISCOSIDADE; [en] VISCOSITY; [pt] REGULARIDADE; [en] REGULARITY; [pt] MULTIPLICIDADE DE SOLUCOES; [en] MULTIPLICITY OF SOLUTIONS; [pt] ESTIMATIVAS A PRIORI; [en] A PRIORI ESTIMATES

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APA (6^th Edition):

NORNBERG, G. S. (2019). [en] METHODS OF THE REGULARITY THEORY IN THE STUDY OF PARTIAL DIFFERENTIAL EQUATIONS WITH NATURAL GROWTH IN THE GRADIENT. (Thesis). Pontifical Catholic University of Rio de Janeiro. Retrieved from http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36015

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

NORNBERG, GABRIELLE SALLER. “[en] METHODS OF THE REGULARITY THEORY IN THE STUDY OF PARTIAL DIFFERENTIAL EQUATIONS WITH NATURAL GROWTH IN THE GRADIENT.” 2019. Thesis, Pontifical Catholic University of Rio de Janeiro. Accessed April 12, 2021. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36015.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

NORNBERG, GABRIELLE SALLER. “[en] METHODS OF THE REGULARITY THEORY IN THE STUDY OF PARTIAL DIFFERENTIAL EQUATIONS WITH NATURAL GROWTH IN THE GRADIENT.” 2019. Web. 12 Apr 2021.

Vancouver:

NORNBERG GS. [en] METHODS OF THE REGULARITY THEORY IN THE STUDY OF PARTIAL DIFFERENTIAL EQUATIONS WITH NATURAL GROWTH IN THE GRADIENT. [Internet] [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2019. [cited 2021 Apr 12]. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36015.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

NORNBERG GS. [en] METHODS OF THE REGULARITY THEORY IN THE STUDY OF PARTIAL DIFFERENTIAL EQUATIONS WITH NATURAL GROWTH IN THE GRADIENT. [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2019. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36015

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

7. Nascimento, Moisés Aparecido do. Resultados do tipo Ambrosetti-Prodi para problemas quasilineares.

Degree: 2015, Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar

URL: https://repositorio.ufscar.br/handle/ufscar/7640

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

We present results of Ambrosseti-Prodi type to quasilinear problems involving the p-Laplace operator. We consider the… (more)

Subjects/Keywords: Grau de Leray-Schauder; Estimativas a priori; p-Laplaciano; Problemas de Neumann; Problemas de Dirichlet; A priori estimates; Quasilinear systems; CIENCIAS EXATAS E DA TERRA::MATEMATICA

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APA (6^th Edition):

Nascimento, M. A. d. (2015). Resultados do tipo Ambrosetti-Prodi para problemas quasilineares. (Doctoral Dissertation). Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar. Retrieved from https://repositorio.ufscar.br/handle/ufscar/7640

Chicago Manual of Style (16^th Edition):

Nascimento, Moisés Aparecido do. “Resultados do tipo Ambrosetti-Prodi para problemas quasilineares.” 2015. Doctoral Dissertation, Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar. Accessed April 12, 2021. https://repositorio.ufscar.br/handle/ufscar/7640.

MLA Handbook (7^th Edition):

Nascimento, Moisés Aparecido do. “Resultados do tipo Ambrosetti-Prodi para problemas quasilineares.” 2015. Web. 12 Apr 2021.

Vancouver:

Nascimento MAd. Resultados do tipo Ambrosetti-Prodi para problemas quasilineares. [Internet] [Doctoral dissertation]. Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar; 2015. [cited 2021 Apr 12]. Available from: https://repositorio.ufscar.br/handle/ufscar/7640.

Council of Science Editors:

Nascimento MAd. Resultados do tipo Ambrosetti-Prodi para problemas quasilineares. [Doctoral Dissertation]. Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar; 2015. Available from: https://repositorio.ufscar.br/handle/ufscar/7640

Universidade Estadual de Campinas

8. Schmidt, Fabiano, 1989-. Estimação de estado regularizada para sistemas de energia elétrica.

Degree: Faculdade de Engenharia Elétrica e de Computação; Programa de Pós-Graduação em Engenharia Elétrica, 2013, Universidade Estadual de Campinas

URL: SCHMIDT, Fabiano. Estimação de estado regularizada para sistemas de energia elétrica. 2013. 105 p. Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/259526>. Acesso em: 23 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/259526

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Orientador: Madson Cortes de Almeida

Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação

Made available in DSpace on 2018-08-23T14:17:23Z… (more)

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Orientador: Madson Cortes de Almeida

Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação

Made available in DSpace on 2018-08-23T14:17:23Z (GMT). No. of bitstreams: 1 Schmidt_Fabiano_M.pdf: 1011600 bytes, checksum: d02fbe7d42a25cfc2745ce47bff3b467 (MD5) Previous issue date: 2013

Resumo: A estimação de estado em sistemas de energia elétrica pode ser descrita como um conjunto de funções que visam fornecer o modelo em tempo real do sistema elétrico. Fazem parte do modelo, a topologia da rede, seus parâmetros elétricos e as variáveis de estado, frequentemente definidas como os fasores de tensões nas barras do sistema. Na obtenção das variáveis de estado, embora os sistemas de medição possam ser projetados para que a rede seja sempre observável, eventualmente, falhas de comunicação, mudanças topológicas ou falhas em medidores podem tornar a rede temporariamente não observável. Nessas situações, as equações normais do modelo de estimação por mínimos quadrados tornam-se mal postas inviabilizando a estimação do estado. Convencionalmente, esse problema é contornado através da restauração da observabilidade, onde pseudomedidas são adicionadas à rede tornando-a novamente observável. Esta dissertação trata da estimação de estado regularizada, que é um método alternativo para lidar com os problemas associados a não observabilidade temporária da rede. Com o estimador regularizado é possível evitar a etapa de restauração da observabilidade, simplificando o processo de estimação de estado. O esquema de regularização adotado é baseado na regularização de Tikhonov, que consiste na introdução de um conjunto de informações a priori que tornam o problema sempre factível. Esse conjunto de informações a priori é obtido da melhor estimativa conhecida para o estado da rede ou a partir de previsões baseadas no conhecimento do comportamento histórico da rede. Ao regularizar o problema, é desejável que o conjunto de informações introduzidas não deteriore a qualidade do estado estimado. Para tanto, deve haver um compromisso entre a qualidade das informações a priori e a suas respectivas ponderações. O uso de ponderações inadequadas pode deteriorar o estado estimado ou piorar o condicionamento numérico das matrizes envolvidas, dificultando a convergência do estimador regularizado. Tais problemas são estudados nesta dissertação. O método de regularização foi desenvolvido nas versões completa e desacoplada que foram combinadas em dois algoritmos visando melhorar as características de convergência do estimador regularizado. As versões desenvolvidas foram testadas com as redes de 14 e 118 barras do Institute of Electrical and Electronics Engineers (IEEE)

Power system state estimation can be described as a set of functions aimed to provide a real time power system electrical model. This model is composed of the network topology, its electrical parameters and a set of state variables, often defined as the bus voltage phasors. In obtaining of the state variables, although the…

Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS, Almeida, Madson Cortes de, 1973-, Mantovani, Jose Roberto Sanches, Junior, Carlos Alberto de Castro.

Subjects/Keywords: Sistemas de energia elétrica; Mínimos quadrados; Teoria da estimativa; Estimativas a-priori; Observadores (Teoria do controle); Power systems; Least squares; Estimation theory; A priori estimates

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APA (6^th Edition):

Schmidt, Fabiano, 1. (2013). Estimação de estado regularizada para sistemas de energia elétrica. (Masters Thesis). Universidade Estadual de Campinas. Retrieved from SCHMIDT, Fabiano. Estimação de estado regularizada para sistemas de energia elétrica. 2013. 105 p. Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/259526>. Acesso em: 23 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/259526

Chicago Manual of Style (16^th Edition):

Schmidt, Fabiano, 1989-. “Estimação de estado regularizada para sistemas de energia elétrica.” 2013. Masters Thesis, Universidade Estadual de Campinas. Accessed April 12, 2021. SCHMIDT, Fabiano. Estimação de estado regularizada para sistemas de energia elétrica. 2013. 105 p. Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/259526>. Acesso em: 23 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/259526.

MLA Handbook (7^th Edition):

Schmidt, Fabiano, 1989-. “Estimação de estado regularizada para sistemas de energia elétrica.” 2013. Web. 12 Apr 2021.

Vancouver:

Schmidt, Fabiano 1. Estimação de estado regularizada para sistemas de energia elétrica. [Internet] [Masters thesis]. Universidade Estadual de Campinas; 2013. [cited 2021 Apr 12]. Available from: SCHMIDT, Fabiano. Estimação de estado regularizada para sistemas de energia elétrica. 2013. 105 p. Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/259526>. Acesso em: 23 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/259526.

Council of Science Editors:

Schmidt, Fabiano 1. Estimação de estado regularizada para sistemas de energia elétrica. [Masters Thesis]. Universidade Estadual de Campinas; 2013. Available from: SCHMIDT, Fabiano. Estimação de estado regularizada para sistemas de energia elétrica. 2013. 105 p. Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/259526>. Acesso em: 23 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/259526

9. G. Romani. Positivity and qualitative properties of solutions of fourth-order elliptic equations.

Degree: 2017, Università degli Studi di Milano

URL: http://hdl.handle.net/2434/525734

► This thesis concerns the study of fourth-order elliptic boundary value problems and, in particular, qualitative properties of solutions. Such problems arise in various fields, from… (more)

Subjects/Keywords: Elliptic Partial Differential Equations; Fourth-order problems; Variational methods; Positivity; A-priori estimates; Settore MAT/05 - Analisi Matematica

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Romani, G. (2017). Positivity and qualitative properties of solutions of fourth-order elliptic equations. (Thesis). Università degli Studi di Milano. Retrieved from http://hdl.handle.net/2434/525734

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Romani, G.. “Positivity and qualitative properties of solutions of fourth-order elliptic equations.” 2017. Thesis, Università degli Studi di Milano. Accessed April 12, 2021. http://hdl.handle.net/2434/525734.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Romani, G.. “Positivity and qualitative properties of solutions of fourth-order elliptic equations.” 2017. Web. 12 Apr 2021.

Vancouver:

Romani G. Positivity and qualitative properties of solutions of fourth-order elliptic equations. [Internet] [Thesis]. Università degli Studi di Milano; 2017. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2434/525734.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Romani G. Positivity and qualitative properties of solutions of fourth-order elliptic equations. [Thesis]. Università degli Studi di Milano; 2017. Available from: http://hdl.handle.net/2434/525734

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Freie Universität Berlin

10. Hardering, Hanne. Intrinsische Diskretisierungsfehlerabschätzungen für Geodätische Finite Elemente.

Degree: 2015, Freie Universität Berlin

URL: https://refubium.fu-berlin.de/handle/fub188/11169

► Die vorliegende Arbeit beschäftigt sich mit dem Beweis optimaler Fehlerschranken für die Diskretisierung H¹-elliptischer Minimisierungsprobleme, deren Lösungen Werte in einer Riemannschen Mannigfaltigkeit annehmen. Die Diskretisierung… (more)

▼ Die vorliegende Arbeit beschäftigt sich mit dem Beweis optimaler Fehlerschranken für die Diskretisierung H¹-elliptischer Minimisierungsprobleme, deren Lösungen Werte in einer Riemannschen Mannigfaltigkeit annehmen. Die Diskretisierung wird dabei mithilfe Geodätischer Finiter Elemente durchgeführt, welche eine unter Isometrien invariante Methode beliebiger Ordnung darstellen. Der Diskretisierungsfehler wird sowohl intrinsisch in einer speziell eingeführten Sobolev-Distanz als auch extrinsisch betrachtet und es werden optimale Abschätzungen vom H¹- und L²-Typ hergeleitet, die in vorausgegangenen Arbeiten anderer Autoren experimentell beobachtet wurden. Unter Verwendung der Rothe-Methode bestehend aus einem impliziten Eulerverfahren zur Zeitdiskretisierung und Geodätischen Finiten Elementen zur Ortsdiskretisierung werden zusätzlich Fehlerabschätzungen für L²-Gradientenflüsse H¹-elliptischer Energien hergeleitet. Kern der Arbeit bilden die Diskretisierungsfehlerabschätzungen für Minimisierungsprobleme in intrinsischen H¹- und L²-Distanzen. Zu deren Herleitung werden zunächst inverse Abschätzungen sowie Interpolationsfehler für Geodätische Finite Elemente und deren diskrete Variationen gezeigt. Unter Verwendung eines nichtlinearen Cea-Lemmas werden daraus H¹-Diskretisierungsfehler für Minimierer H¹-elliptischer Energien hergeleitet. Mit Hilfe einer Verallgemeinerung des Aubin-Nitsche-Lemmas werden sodann für (im Wesentlichen) semilineare Energien auch optimale L²-Fehlerschranken gezeigt, wobei aus technischen Gründen die Dimension des Definitionsgebietes des Minimierers auf d<4 beschränkt wird. Alle Resultate werden anhand von harmonischen Abbildungen in eine glatte Riemannsche Mannigfaltigkeit, welche gewisse Krümmungsschranken erfüllt, illustriert. Advisors/Committee Members: [email protected] (contact), w (gender), Prof. Dr. Ralf Kornhuber (firstReferee), Prof. Dr. Sören Bartels (furtherReferee), Prof. Dr. Gerhard Huisken (furtherReferee).

Subjects/Keywords: Geodesic Finite Elements; A priori error estimates; 500 Naturwissenschaften und Mathematik::510 Mathematik::518 Numerische Analysis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hardering, H. (2015). Intrinsische Diskretisierungsfehlerabschätzungen für Geodätische Finite Elemente. (Thesis). Freie Universität Berlin. Retrieved from https://refubium.fu-berlin.de/handle/fub188/11169

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Hardering, Hanne. “Intrinsische Diskretisierungsfehlerabschätzungen für Geodätische Finite Elemente.” 2015. Thesis, Freie Universität Berlin. Accessed April 12, 2021. https://refubium.fu-berlin.de/handle/fub188/11169.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Hardering, Hanne. “Intrinsische Diskretisierungsfehlerabschätzungen für Geodätische Finite Elemente.” 2015. Web. 12 Apr 2021.

Vancouver:

Hardering H. Intrinsische Diskretisierungsfehlerabschätzungen für Geodätische Finite Elemente. [Internet] [Thesis]. Freie Universität Berlin; 2015. [cited 2021 Apr 12]. Available from: https://refubium.fu-berlin.de/handle/fub188/11169.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hardering H. Intrinsische Diskretisierungsfehlerabschätzungen für Geodätische Finite Elemente. [Thesis]. Freie Universität Berlin; 2015. Available from: https://refubium.fu-berlin.de/handle/fub188/11169

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Brunel University

11. Al-Shanfari, Fatima. High-order in time discontinuous Galerkin finite element methods for linear wave equations.

Degree: PhD, 2017, Brunel University

URL: http://bura.brunel.ac.uk/handle/2438/15332 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764823

► In this thesis we analyse the high-order in time discontinuous Galerkin nite element method (DGFEM) for second-order in time linear abstract wave equations. Our abstract… (more)

▼ In this thesis we analyse the high-order in time discontinuous Galerkin nite element method (DGFEM) for second-order in time linear abstract wave equations. Our abstract approximation analysis is a generalisation of the approach introduced by Claes Johnson (in Comput. Methods Appl. Mech. Engrg., 107:117-129, 1993), writing the second order problem as a system of fi rst order problems. We consider abstract spatial (time independent) operators, highorder in time basis functions when discretising in time; we also prove approximation results in case of linear constraints, e.g. non-homogeneous boundary data. We take the two steps approximation approach i.e. using high-order in time DGFEM; the discretisation approach in time introduced by D Schötzau (PhD thesis, Swiss Federal institute of technology, Zürich, 1999) to fi rst obtain the semidiscrete scheme and then conformal spatial discretisation to obtain the fully-discrete formulation. We have shown solvability, unconditional stability and conditional a priori error estimates within our abstract framework for the fully discretized problem. The skew-symmetric spatial forms arising in our abstract framework for the semi- and fully-discrete schemes do not full ll the underlying assumptions in D. Schötzau's work. But the semi-discrete and fully discrete forms satisfy an Inf-sup condition, essential for our proofs; in this sense our approach is also a generalisation of D. Schötzau's work. All estimates are given in a norm in space and time which is weaker than the Hilbert norm belonging to our abstract function spaces, a typical complication in evolution problems. To the best of the author's knowledge, with the approximation approach we used, these stability and a priori error estimates with their abstract structure have not been shown before for the abstract variational formulation used in this thesis. Finally we apply our abstract framework to the acoustic and an elasto-dynamic linear equations with non-homogeneous Dirichlet boundary data.

Subjects/Keywords: 519.2; Second-order in time evolution problems; Stability estimates in abstract Hilbert spaces; Inf-sup condition theorem; Linear wave equations with constraints; A priori error estimates

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Al-Shanfari, F. (2017). High-order in time discontinuous Galerkin finite element methods for linear wave equations. (Doctoral Dissertation). Brunel University. Retrieved from http://bura.brunel.ac.uk/handle/2438/15332 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764823

Chicago Manual of Style (16^th Edition):

Al-Shanfari, Fatima. “High-order in time discontinuous Galerkin finite element methods for linear wave equations.” 2017. Doctoral Dissertation, Brunel University. Accessed April 12, 2021. http://bura.brunel.ac.uk/handle/2438/15332 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764823.

MLA Handbook (7^th Edition):

Al-Shanfari, Fatima. “High-order in time discontinuous Galerkin finite element methods for linear wave equations.” 2017. Web. 12 Apr 2021.

Vancouver:

Al-Shanfari F. High-order in time discontinuous Galerkin finite element methods for linear wave equations. [Internet] [Doctoral dissertation]. Brunel University; 2017. [cited 2021 Apr 12]. Available from: http://bura.brunel.ac.uk/handle/2438/15332 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764823.

Council of Science Editors:

Al-Shanfari F. High-order in time discontinuous Galerkin finite element methods for linear wave equations. [Doctoral Dissertation]. Brunel University; 2017. Available from: http://bura.brunel.ac.uk/handle/2438/15332 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.764823

University of Tennessee – Knoxville

12. Wise, Michael Morgan. Finite element methods for nonlinear, dispersive equations.

Degree: 2020, University of Tennessee – Knoxville

URL: https://trace.tennessee.edu/utk_graddiss/5898

► The present study is concerned with the numerical approximation of solutions of systems of Korteweg-de Vries type, coupled through their nonlinear terms. We construct, analyze,… (more)

Subjects/Keywords: finite element methods; discontinuous Galerkin methods; Korteweg-de Vries equation; a priori; error estimates; a posteriori; conservation laws; dispersive equations; nonlinear equations; adaptive methods

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wise, M. M. (2020). Finite element methods for nonlinear, dispersive equations. (Doctoral Dissertation). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_graddiss/5898

Chicago Manual of Style (16^th Edition):

Wise, Michael Morgan. “Finite element methods for nonlinear, dispersive equations.” 2020. Doctoral Dissertation, University of Tennessee – Knoxville. Accessed April 12, 2021. https://trace.tennessee.edu/utk_graddiss/5898.

MLA Handbook (7^th Edition):

Wise, Michael Morgan. “Finite element methods for nonlinear, dispersive equations.” 2020. Web. 12 Apr 2021.

Vancouver:

Wise MM. Finite element methods for nonlinear, dispersive equations. [Internet] [Doctoral dissertation]. University of Tennessee – Knoxville; 2020. [cited 2021 Apr 12]. Available from: https://trace.tennessee.edu/utk_graddiss/5898.

Council of Science Editors:

Wise MM. Finite element methods for nonlinear, dispersive equations. [Doctoral Dissertation]. University of Tennessee – Knoxville; 2020. Available from: https://trace.tennessee.edu/utk_graddiss/5898

Pontifical Catholic University of Rio de Janeiro

13. DANIA GONZALEZ MORALES. [en] TWO TOPICS IN DEGENERATE ELLIPTIC EQUATIONS INVOLVING A GRADIENT TERM: EXISTENCE OF SOLUTIONS AND A PRIORI ESTIMATES.

Degree: 2019, Pontifical Catholic University of Rio de Janeiro

URL: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36440

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[pt] Esta tese tem o intuito do estudo da existência, não existência e estimativas a priori de soluções não negativas de alguns tipos de problemas… (more)

Subjects/Keywords: [pt] EXISTENCIA; [en] EXISTENCE; [pt] ESTIMATIVAS A PRIORI; [en] A PRIORI ESTIMATES; [pt] NAO EXISTENCIA; [en] NON EXISTENCE; [pt] EDPS DEGENERADAS; [en] DEGENERATE PDES; [pt] P-LAPLACIANO; [en] P-LAPLACIAN; [pt] DEPENDENCIA DO GRADIENTE; [en] DEPENDENCE ON THE GRADIENT; [pt] CONDICOES INTEGRAIS KELLER-OSSERMAN; [en] KELLER-OSSERMAN INTEGRAL CONDITIONS; [pt] ESTIMATIVAS ATE A FRONTEIRA; [en] BOUNDARY ESTIMATES

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

MORALES, D. G. (2019). [en] TWO TOPICS IN DEGENERATE ELLIPTIC EQUATIONS INVOLVING A GRADIENT TERM: EXISTENCE OF SOLUTIONS AND A PRIORI ESTIMATES. (Thesis). Pontifical Catholic University of Rio de Janeiro. Retrieved from http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36440

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

MORALES, DANIA GONZALEZ. “[en] TWO TOPICS IN DEGENERATE ELLIPTIC EQUATIONS INVOLVING A GRADIENT TERM: EXISTENCE OF SOLUTIONS AND A PRIORI ESTIMATES.” 2019. Thesis, Pontifical Catholic University of Rio de Janeiro. Accessed April 12, 2021. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36440.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

MORALES, DANIA GONZALEZ. “[en] TWO TOPICS IN DEGENERATE ELLIPTIC EQUATIONS INVOLVING A GRADIENT TERM: EXISTENCE OF SOLUTIONS AND A PRIORI ESTIMATES.” 2019. Web. 12 Apr 2021.

Vancouver:

MORALES DG. [en] TWO TOPICS IN DEGENERATE ELLIPTIC EQUATIONS INVOLVING A GRADIENT TERM: EXISTENCE OF SOLUTIONS AND A PRIORI ESTIMATES. [Internet] [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2019. [cited 2021 Apr 12]. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36440.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

MORALES DG. [en] TWO TOPICS IN DEGENERATE ELLIPTIC EQUATIONS INVOLVING A GRADIENT TERM: EXISTENCE OF SOLUTIONS AND A PRIORI ESTIMATES. [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2019. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36440

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

14. Clérin, Jean-Marc. Problèmes de contrôle optimal du type bilinéaire gouvernés par des équations aux dérivées partielles d’évolution : Analysis of bilinear optimal control problems governed by evolution partial differential equations.

Degree: Docteur es, Mathématiques appliquées et applications des mathématiques, 2009, Avignon

URL: http://www.theses.fr/2009AVIG0405

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Cette thèse est une contribution à l’étude de problèmes de contrôle optimal dont le caractère non linéaire se traduit par la présence, dans les équations… (more)

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Cette thèse est une contribution à l’étude de problèmes de contrôle optimal dont le caractère non linéaire se traduit par la présence, dans les équations d’état, d’un terme bilinéaire relativement à l’état et au contrôle. Malgré les difficultés liées à la non linéarité, nous obtenons des propriétés spécifiques au cas bilinéaire. L’introduction générale constitue la première partie. La seconde partie est consacrée à l’étude des équations d’état ; ce sont des équations aux dérivées partielles d’évolution. Nous établissons des estimations a priori sur les solutions à partir des inégalités de Willett et Wong et nous démontrons que les équations d’états sont bien posées. Dans le cas où les contrôles subissent une contrainte liée aux états, ces estimations permettent de déduire l’existence de solutions dans le cadre des inclusions différentielles. Les troisième et quatrième parties de ce mémoire sont dévolues à la démonstration de l’existence de contrôles optimaux, puis à l’analyse de la sensibilité relative à une perturbation qui intervient de façon additive dans l’équation d’état. Le caractère bilinéaire permet de vérifier des conditions suffisantes d’optimalité du second ordre. Nous fournissons sur des exemples, une formule explicite des dérivées directionnelles de la fonction valeur optimale

This thesis is devoted to the analysis of nonlinear optimal control problems governed by an evolution state equation involving a term which is bilinear in state and control. The difficulties due to nonlinearity remain, but bilinearity adds a lot of structure to the control problem under consideration. In Section 2, by using Willet and Wong inequalities we establish a priori estimates for the solutions of the state equation. These estimates allow us to prove that the state equation is well posed in the sense of Hadamard. In the case of a feedback constraint on the control, the state equation becomes a differential inclusion. Under mild assumptions, such a differential inclusion is solvable. In Section 3, we prove the existence of solutions to the optimal control problem. Section 4 is devoted to the sensitivity analysis of the optimal control problem. We obtain a formula for the directional derivative of the optimal value function. This general formula is worked out in detail for particular examples

Advisors/Committee Members: Moussaoui, Mohammed (thesis director).

Subjects/Keywords: Contrôle optimal bilinéaire; Estimations a priori; Inclusions différentielles; Problèmes d’évolution bien posés; Lois de feedback; Systèmes non linéaires de dimension infinie; Sensibilité; Régularité forte; Bilinear optimal control; A priori estimates; Differential inclusion; Well posed evolution problem; Feedback control; Nonlinear infinite system; Sensitivity; Strong regularity

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Clérin, J. (2009). Problèmes de contrôle optimal du type bilinéaire gouvernés par des équations aux dérivées partielles d’évolution : Analysis of bilinear optimal control problems governed by evolution partial differential equations. (Doctoral Dissertation). Avignon. Retrieved from http://www.theses.fr/2009AVIG0405

Chicago Manual of Style (16^th Edition):

Clérin, Jean-Marc. “Problèmes de contrôle optimal du type bilinéaire gouvernés par des équations aux dérivées partielles d’évolution : Analysis of bilinear optimal control problems governed by evolution partial differential equations.” 2009. Doctoral Dissertation, Avignon. Accessed April 12, 2021. http://www.theses.fr/2009AVIG0405.

MLA Handbook (7^th Edition):

Clérin, Jean-Marc. “Problèmes de contrôle optimal du type bilinéaire gouvernés par des équations aux dérivées partielles d’évolution : Analysis of bilinear optimal control problems governed by evolution partial differential equations.” 2009. Web. 12 Apr 2021.

Vancouver:

Clérin J. Problèmes de contrôle optimal du type bilinéaire gouvernés par des équations aux dérivées partielles d’évolution : Analysis of bilinear optimal control problems governed by evolution partial differential equations. [Internet] [Doctoral dissertation]. Avignon; 2009. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2009AVIG0405.

Council of Science Editors:

Clérin J. Problèmes de contrôle optimal du type bilinéaire gouvernés par des équations aux dérivées partielles d’évolution : Analysis of bilinear optimal control problems governed by evolution partial differential equations. [Doctoral Dissertation]. Avignon; 2009. Available from: http://www.theses.fr/2009AVIG0405

Universidade Estadual de Campinas

15. Junges-Miotto, Taisa. Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares.

Degree: Instituto de Matemática, Estatística e Computação Científica; Programa de Pós-Graduação em Matemática, 2009, Universidade Estadual de Campinas

URL: JUNGES-MIOTTO, Taisa. Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares. 2009. 74 f. Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/306984>. Acesso em: 13 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/306984

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Orientadores: Djairo Guedes de Figueiredo, Olimpio Hiroshi Miyagaki

Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica

Made available in… (more)

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Orientadores: Djairo Guedes de Figueiredo, Olimpio Hiroshi Miyagaki

Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica

Made available in DSpace on 2018-08-13T07:50:56Z (GMT). No. of bitstreams: 1 Junges-Miotto_Taisa_D.pdf: 1407780 bytes, checksum: c2871097b4e97e35198b351dbcfa999b (MD5) Previous issue date: 2009

Resumo: O objetivo deste trabalho é obter estimativas ABP para operadores completamente não lineares e estudar problemas do tipo Ambrosetti-Prodi para o operador p-Laplaciano nos casos superlinear para a equação e sublinear para sistema, aplicando o método de sub e supersolução e a teoria do grau de Leray Schauder, para obtermos nos casos de Ambrosetti-Prodi, multiplicidade de soluções. Para aplicarmos a teoria do grau de Leray Schauder precisamos obter estimativas a priori das eventuais soluções dos problemas, estimativas essas que serão obtidas aplicando-se técnicas diferentes em cada caso. No Capítulo 1 enunciaremos alguns resultados auxiliares que serão utilizados no decorrer do trabalho. No Capítulo 2 obtemos estimativas do tipo ABP para soluções de viscosidade de uma classe de operadores completamente não lineares, o qual um exemplo é o operador p-Laplaciano. No Capítulo 3 estudamos o problema do tipo Ambrosetti-Prodi para equação com o p-Laplaciano no caso superlinear, fazendo uso da técnica blow up e de teoremas do tipo Liouville. No Capítulo 4 estudamos o problema do tipo Ambrosetti-Prodi para sistema com o p-Laplaciano no caso sublinear, utilizando para isso soluções de viscosidade e a caracterização do autovalor principal.

The aim of this work is to obtain ABP estimates for fully nonlinear operators and to study problems of the Ambrosetti-Prodi type for the p-Laplacian operator in two cases: superlinear case for the equation and the sublinear case for the system. For this, we use the sub and supersolution method and the Leray Schauder degree theory, to obtain in the two cases, multiplicity of solutions. To apply the degree theory, we need a priori estimates of the possible solutions, obtained applying di_erent techniques in each problem. In Chapter 1 we will cite some auxiliary results, which will use during this work. In Chapter 2 we will obtain ABP estimates for viscosity solutions to a class of fully nonlinear operators, whose example is the p_Laplacian operator. In Chapter 3 we will study the Ambrosetti-Prodi type problems for the superlinear case, using the blow up technique and Liouville theorems type. In Chapter 4 we will study the Ambrosetti-Prodi type problem for system in the sublinear case, using for this viscosity solutions and the variational characterization of the principal eigenvalue.

Doutorado

Doutor em Matemática

Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS, Miyagaki, Olimpio Hiroshi, Figueiredo, Djairo Guedes de, 1934-, Montenegro, Marcelo da Silva, Filho, Milton da Costa Lopes, Teixeira, Eduardo Vasconcelos Oliveira, Barrera, Andres Avila.

Subjects/Keywords: Equações diferenciais parciais; Equações diferenciais não-lineares; Estimativas a-priori; Partial differential equations; Nonlinear differential equations; A priori estimates

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APA (6^th Edition):

Junges-Miotto, T. (2009). Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares. (Doctoral Dissertation). Universidade Estadual de Campinas. Retrieved from JUNGES-MIOTTO, Taisa. Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares. 2009. 74 f. Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/306984>. Acesso em: 13 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/306984

Chicago Manual of Style (16^th Edition):

Junges-Miotto, Taisa. “Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares.” 2009. Doctoral Dissertation, Universidade Estadual de Campinas. Accessed April 12, 2021. JUNGES-MIOTTO, Taisa. Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares. 2009. 74 f. Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/306984>. Acesso em: 13 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/306984.

MLA Handbook (7^th Edition):

Junges-Miotto, Taisa. “Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares.” 2009. Web. 12 Apr 2021.

Vancouver:

Junges-Miotto T. Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares. [Internet] [Doctoral dissertation]. Universidade Estadual de Campinas; 2009. [cited 2021 Apr 12]. Available from: JUNGES-MIOTTO, Taisa. Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares. 2009. 74 f. Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/306984>. Acesso em: 13 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/306984.

Council of Science Editors:

Junges-Miotto T. Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares. [Doctoral Dissertation]. Universidade Estadual de Campinas; 2009. Available from: JUNGES-MIOTTO, Taisa. Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares. 2009. 74 f. Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica, Campinas, SP. Disponível em: <http://www.repositorio.unicamp.br/handle/REPOSIP/306984>. Acesso em: 13 ago. 2018. ; http://repositorio.unicamp.br/jspui/handle/REPOSIP/306984

16. Lima, Lucas Fabiano. A mean-field game model of economic growth : an essay in regularity theory.

Degree: 2016, Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar

URL: https://repositorio.ufscar.br/handle/ufscar/8902

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

In this thesis, we present a priori estimates for solutions of a mean-field game (MFG) defined over… (more)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

In this thesis, we present a priori estimates for solutions of a mean-field game (MFG) defined over a bounded domain Ω ⊂ ℝd. We propose an application of these results to a model of capital and wealth accumulation. In Chapter 1, an introduction to mean-field games is presented. We also put forward some of the motivation from Economics and discuss previous developments in the theory of differential games. These comments aim at indicating the connection between mean-field games theory, its applications and the realm of Mathematical Analysis. In Chapter 2, we present an optimal control problem. Here, the agents are supposed to be undistinguishable, rational and intelligent. Undistinguishable means that every agent is governed by the same stochastic differential equation. Rational means that all efforts of the agent is to maximize a payoff functional. Intelligent means that they are able to solve an optimal control problem. Once we describe this (stochastic) optimal control problem, we produce a heuristic derivation of the mean-field games system, which is summarized in a Verification Theorem; this gives rise to the Hamilton-Jacobi equation (HJ). After that, we obtain the Fokker-Plank equation (FP). Finally, we present a representation formula for the solutions to the (HJ) equation, together with some regularity results. In Chapter 3, a specific optimal control problem is described and the associated MFG is presented. This MFG is prescribed in a bounded domain Ω ⊂ ℝd, which introduces substantialadditional challenges from the mathematical view point. This is due to estimates for the solutionsat the boundary in Lp. The rest of the chapter puts forward two well known tips of estimates: theso-called Hopf-Lax formula and the First Order Estimate. In Chapter 4, the wealth and capital accumulation mean-field game model is presented. The relevance of studying MFG in a bounded domain then becomes clear. In light of the results obtained in Chapter 3, we close Chapter 4 with the Hopf-Lax formula, and the First Order estimates. Three appendices close this thesis. They gather elementary material on Stochastic Calculus and Functional Analysis.

Nesta dissertação são apresentadas algumas estimativas a priori para soluções de sistemas mean-field games (MFG), definidos em domínios limitados Ω ⊂ ℝd. Tais estimativas são aplicadas em um modelo mean-field específico, que descreve o acúmulo de riqueza e capital. No Capítulo 1, é apresentada uma breve introdução histórica sobre os mean-field games. Nesta introdução, exploramos sua relação com a teoria dos jogos, cujos alicerces foram construídos por economistas e matemáticos ao longo do século XX. O objetivo do capítulo é transmitir. No Capítulo 2, apresentamos um problema de controle ótimo em que cada agente é suposto ser indistinguível, racional e inteligente. Indistinguível no sentido de que cada um é governado pela mesma equação diferencial estocástica. Racional no sentido de que…

Advisors/Committee Members: Pimentel, Edgard Almeida.

Subjects/Keywords: Equação de Hamilton-Jacobi; Equação de Fokker- Planck; Estimativas a priori; Domínios limitados; Método adjunto não-linear; Hamilton-Jacobi equation; Fokker-Plank equation; A priori estimates; Bounded domains; Non-linear adjoint method; Mean-field games; CIENCIAS EXATAS E DA TERRA::MATEMATICA

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lima, L. F. (2016). A mean-field game model of economic growth : an essay in regularity theory. (Masters Thesis). Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar. Retrieved from https://repositorio.ufscar.br/handle/ufscar/8902

Chicago Manual of Style (16^th Edition):

Lima, Lucas Fabiano. “A mean-field game model of economic growth : an essay in regularity theory.” 2016. Masters Thesis, Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar. Accessed April 12, 2021. https://repositorio.ufscar.br/handle/ufscar/8902.

MLA Handbook (7^th Edition):

Lima, Lucas Fabiano. “A mean-field game model of economic growth : an essay in regularity theory.” 2016. Web. 12 Apr 2021.

Vancouver:

Lima LF. A mean-field game model of economic growth : an essay in regularity theory. [Internet] [Masters thesis]. Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar; 2016. [cited 2021 Apr 12]. Available from: https://repositorio.ufscar.br/handle/ufscar/8902.

Council of Science Editors:

Lima LF. A mean-field game model of economic growth : an essay in regularity theory. [Masters Thesis]. Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar; 2016. Available from: https://repositorio.ufscar.br/handle/ufscar/8902

Brunel University

17. Jang, Yongseok. Spatially continuous and discontinuous Galerkin finite element approximations for dynamic viscoelastic problems.

Degree: PhD, 2020, Brunel University

URL: http://bura.brunel.ac.uk/handle/2438/21084 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.814447

Subjects/Keywords: A priori estimates; Power-law; Fractional order viscoelasticity; Generalised Maxwell solid

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Jang, Y. (2020). Spatially continuous and discontinuous Galerkin finite element approximations for dynamic viscoelastic problems. (Doctoral Dissertation). Brunel University. Retrieved from http://bura.brunel.ac.uk/handle/2438/21084 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.814447

Chicago Manual of Style (16^th Edition):

Jang, Yongseok. “Spatially continuous and discontinuous Galerkin finite element approximations for dynamic viscoelastic problems.” 2020. Doctoral Dissertation, Brunel University. Accessed April 12, 2021. http://bura.brunel.ac.uk/handle/2438/21084 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.814447.

MLA Handbook (7^th Edition):

Jang, Yongseok. “Spatially continuous and discontinuous Galerkin finite element approximations for dynamic viscoelastic problems.” 2020. Web. 12 Apr 2021.

Vancouver:

Jang Y. Spatially continuous and discontinuous Galerkin finite element approximations for dynamic viscoelastic problems. [Internet] [Doctoral dissertation]. Brunel University; 2020. [cited 2021 Apr 12]. Available from: http://bura.brunel.ac.uk/handle/2438/21084 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.814447.

Council of Science Editors:

Jang Y. Spatially continuous and discontinuous Galerkin finite element approximations for dynamic viscoelastic problems. [Doctoral Dissertation]. Brunel University; 2020. Available from: http://bura.brunel.ac.uk/handle/2438/21084 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.814447

18. Karolina Barone Ribeiro da Silva. Estimativas de máxima verosimilhança e bayesianas do número de erros de um software.

Degree: 2006, Universidade Federal de São Carlos

URL: http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=1020

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Nesta dissertação apresentamos a metodologia de captura-recaptura, sob os enfoques clássico e bayesiano, para estimar o número de erros de um software através de sua… (more)

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Nesta dissertação apresentamos a metodologia de captura-recaptura, sob os enfoques clássico e bayesiano, para estimar o número de erros de um software através de sua inspeção por revisores distintos. Apresentamos o modelo estatístico geral considerando independência entre erros e entre revisores e consideramos os casos particulares de erros igualmente.detectáveis (homogêneos) e revisores não igualmente eficientes (heterogêneos) e de erros não igualmente detectáveis (heterogêneos) e revisores igualmente eficientes (homogêneos). Em seguida, sob a hipótese de heterogeneidade e independência entre erros e homogeneidade e independência entre revisores, supusemos que a heterogeneidade dos erros era expressa por uma classificação destes em fácil e difícil de detectar, admitindo conhecidas as probabilidades de detecção de um erro fácil e de um erro difícil. Finalmente, sob a hipótese de independência e homogeneidade entre erros, apresentamos um novo modelo considerando heterogeneidade e dependência entre revisores. Além disso, apresentamos exemplos com dados simulados e reais.

In this work we present the methodology of capture-recapture, under the classic and bayesian approach, to estimate the number of errors of software through inspection by distinct reviewers. We present the general statistical model considering independence among errors and among reviewers and consider the particular cases of equally detectable errors (homogeneous) and reviewers not equally e cient (heterogeneous) and of errors not equally detectable (heterogeneous) and equally e cient reviewers (homogeneous). After that, under the assumption of independence and heterogeneity among errors and independence and homogeneity among reviwers, we supposed that the heterogeneity of the errors was expressed by a classification of these in easy and di cult of detecting, admitting known the probabilities of detection of an easy error and of a di cult error. Finally, under the hypothesis of independence and homogeneity among errors, we presented a new model considering heterogeneity and dependence among reviewers. Besides, we presented examples with simulate and real data.

Advisors/Committee Members: José Galvão Leite.

Subjects/Keywords: Estatística matemática; Processo seqüêncial de captura-recaptura; MSMC; Inferência bayesiana; Estimativas de máxima verosimilhança; Capture-recapture process; ESTATISTICA; Software review; Maximum likelihood estimates; A priori and a posteriori distributions; Bayes estimates

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Silva, K. B. R. d. (2006). Estimativas de máxima verosimilhança e bayesianas do número de erros de um software. (Thesis). Universidade Federal de São Carlos. Retrieved from http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=1020

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Silva, Karolina Barone Ribeiro da. “Estimativas de máxima verosimilhança e bayesianas do número de erros de um software.” 2006. Thesis, Universidade Federal de São Carlos. Accessed April 12, 2021. http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=1020.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Silva, Karolina Barone Ribeiro da. “Estimativas de máxima verosimilhança e bayesianas do número de erros de um software.” 2006. Web. 12 Apr 2021.

Vancouver:

Silva KBRd. Estimativas de máxima verosimilhança e bayesianas do número de erros de um software. [Internet] [Thesis]. Universidade Federal de São Carlos; 2006. [cited 2021 Apr 12]. Available from: http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=1020.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Silva KBRd. Estimativas de máxima verosimilhança e bayesianas do número de erros de um software. [Thesis]. Universidade Federal de São Carlos; 2006. Available from: http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=1020

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

19. Tang, Chunquan. Mixed boundary value problems for quasilinear elliptic equations.

Degree: 2013, Iowa State University

URL: https://lib.dr.iastate.edu/etd/13009

► We study the a priori estimates and existence for solutions of mixed boundary value problems for quasilinear elliptic equations. We prove maximum estimates, gradient estimates… (more)

Subjects/Keywords: Angle conditions; A priori estimates; Barrier method; Existence theory; Applied Mathematics; Mathematics

…vii ABSTRACT We study the a priori estimates and existence for solutions of mixed… …We prove various a priori estimates and use them to prove existence theorems. To motivate… …gradient estimates in Chapter 6. Lastly, in Chapter 7, we use these a priori estimates to derive… …hypothesis on aij , a, ϕ, b and Ω to be discussed, we shall prove various a priori estimates for… …In this chapter, we are concerned with the derivation of a priori estimates for the ¯ for…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tang, C. (2013). Mixed boundary value problems for quasilinear elliptic equations. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/13009

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Tang, Chunquan. “Mixed boundary value problems for quasilinear elliptic equations.” 2013. Thesis, Iowa State University. Accessed April 12, 2021. https://lib.dr.iastate.edu/etd/13009.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Tang, Chunquan. “Mixed boundary value problems for quasilinear elliptic equations.” 2013. Web. 12 Apr 2021.

Vancouver:

Tang C. Mixed boundary value problems for quasilinear elliptic equations. [Internet] [Thesis]. Iowa State University; 2013. [cited 2021 Apr 12]. Available from: https://lib.dr.iastate.edu/etd/13009.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Tang C. Mixed boundary value problems for quasilinear elliptic equations. [Thesis]. Iowa State University; 2013. Available from: https://lib.dr.iastate.edu/etd/13009

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

20. Mirabito, Christopher Michael. Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation.

Degree: PhD, Computational and Applied Mathematics, 2011, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2011-08-4130

► Storm surge, the pileup of seawater occurring as a result of high surface stresses and strong currents generated by extreme storm events such as hurricanes,… (more)

▼ Storm surge, the pileup of seawater occurring as a result of high surface stresses and strong currents generated by extreme storm events such as hurricanes, is known to cause greater loss of life than these storms' associated winds. For example, inland flooding from the storm surge along the Gulf Coast during Hurricane Katrina killed hundreds of people. Previous storms produced even larger death tolls. Simultaneously, dune, barrier island, and channel erosion taking place during a hurricane leads to the removal of major flow controls, which significantly affects inland inundation. Also, excessive sea bed scouring around pilings can compromise the structural integrity of bridges, levees, piers, and buildings. Modeling these processes requires tightly coupling a bed morphology equation to the shallow water equations (SWE). Discontinuous Galerkin finite element methods (DGFEMs) are a natural choice for modeling this coupled system, given the need to solve these problems on large, complicated, unstructured computational meshes, as well as the desire to implement hp-adaptivity for capturing the dynamic features of the solution. Comprehensive modeling of these processes in the coastal zone presents several challenges and open questions. Most existing hydrodynamic models use a fixed-bed approach; the bottom is not allowed to evolve in response to the fluid motion. With respect to movable-bed models, there is no single, generally accepted mathematical model in use. Numerical challenges include coupling models of processes that exhibit disparate time scales during fair weather, but possibly similar time scales during intense storms. The main goals of this dissertation include implementing a robust, efficient, tightly-coupled morphological model using the local discontinuous Galerkin (LDG) method within the existing Advanced Circulation (ADCIRC) modeling framework, performing systematic code and model verification (using test cases with known solutions, proven convergence rates, or well-documented physical behavior), analyzing the stability and accuracy of the implemented numerical scheme by way of a priori error estimates, and ultimately laying some of the necessary groundwork needed to simultaneously model storm surges and bed morphodynamics during extreme storm events. Advisors/Committee Members: Dawson, Clinton N. (advisor), Demkowicz, Leszek F. (committee member), Gamba, Irene M. (committee member), Ghattas, Omar (committee member), Kim, Wonsuck (committee member).

Subjects/Keywords: Shallow water equations; Sediment transport; Local discontinuous Galerkin; A priori estimates; Finite elements; Bed morphology

…of a priori error estimates, and ultimately laying some of the necessary groundwork needed… …Chapter 3. An A Priori Error Estimate 3.1 The Error Equation… …height, to be known a priori ; in practice, these would need to be calculated using analytical… …priori error estimate for a slightly simplified form of this system has been derived (see… …several challenges and open questions. Most existing hydrodynamic models use a fixed-bed…

10 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mirabito, C. M. (2011). Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2011-08-4130

Chicago Manual of Style (16^th Edition):

Mirabito, Christopher Michael. “Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation.” 2011. Doctoral Dissertation, University of Texas – Austin. Accessed April 12, 2021. http://hdl.handle.net/2152/ETD-UT-2011-08-4130.

MLA Handbook (7^th Edition):

Mirabito, Christopher Michael. “Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation.” 2011. Web. 12 Apr 2021.

Vancouver:

Mirabito CM. Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2011. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2152/ETD-UT-2011-08-4130.

Council of Science Editors:

Mirabito CM. Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation. [Doctoral Dissertation]. University of Texas – Austin; 2011. Available from: http://hdl.handle.net/2152/ETD-UT-2011-08-4130

21. Kalappattil, Lakshmi Sankar. Classes of singular nonlinear eigenvalue problems with semipositone structure.

Degree: PhD, Mathematics and Statistics, 2013, Mississippi State University

URL: http://sun.library.msstate.edu/ETD-db/theses/available/etd-04262013-061925/ ;

► The investigation of positive steady states to reaction diffusion models in bounded domains with Dirichlet boundary conditions has been of great interest since the… (more)

Subjects/Keywords: A priori estimates; Method of sub and super solutions; Uniqueness results; Existence results; Exterior Domains; Semipositone; Boundary value problems

…4.2 A priori estimates . . . . . . . . . . . . . . . . . . . . . . . . . . Proof of Theorem… …results by establishing a priori estimates and analyzing structural properties of solutions. 3… …The method of sub and super solutions . . . . . . . . . . . . . . . A sweeping principle… …The reduction of an exterior domain problem to a two point boundary value problem… …32 4.2 A solution with more than one maximum . . . . . . . . . . . . . . . . . . 33 4.3…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kalappattil, L. S. (2013). Classes of singular nonlinear eigenvalue problems with semipositone structure. (Doctoral Dissertation). Mississippi State University. Retrieved from http://sun.library.msstate.edu/ETD-db/theses/available/etd-04262013-061925/ ;

Chicago Manual of Style (16^th Edition):

Kalappattil, Lakshmi Sankar. “Classes of singular nonlinear eigenvalue problems with semipositone structure.” 2013. Doctoral Dissertation, Mississippi State University. Accessed April 12, 2021. http://sun.library.msstate.edu/ETD-db/theses/available/etd-04262013-061925/ ;.

MLA Handbook (7^th Edition):

Kalappattil, Lakshmi Sankar. “Classes of singular nonlinear eigenvalue problems with semipositone structure.” 2013. Web. 12 Apr 2021.

Vancouver:

Kalappattil LS. Classes of singular nonlinear eigenvalue problems with semipositone structure. [Internet] [Doctoral dissertation]. Mississippi State University; 2013. [cited 2021 Apr 12]. Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-04262013-061925/ ;.

Council of Science Editors:

Kalappattil LS. Classes of singular nonlinear eigenvalue problems with semipositone structure. [Doctoral Dissertation]. Mississippi State University; 2013. Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-04262013-061925/ ;

22. Silva, Karolina Barone Ribeiro da. Estimativas de máxima verosimilhança e bayesianas do número de erros de um software.

Degree: 2006, Universidade Federal de São Carlos; Programa de Pós-Graduação em Estatística – PPGEs; UFSCar; BR

URL: https://repositorio.ufscar.br/handle/ufscar/4498

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In this work we present the methodology of capture-recapture, under the classic and bayesian approach, to estimate the number of errors of software through inspection… (more)

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In this work we present the methodology of capture-recapture, under the classic and bayesian approach, to estimate the number of errors of software through inspection by distinct reviewers. We present the general statistical model considering independence among errors and among reviewers and consider the particular cases of equally detectable errors (homogeneous) and reviewers not equally e¢ cient (heterogeneous) and of errors not equally detectable (heterogeneous) and equally e¢ cient reviewers (homogeneous). After that, under the assumption of independence and heterogeneity among errors and independence and homogeneity among reviwers, we supposed that the heterogeneity of the errors was expressed by a classification of these in easy and di¢ cult of detecting, admitting known the probabilities of detection of an easy error and of a di¢ cult error. Finally, under the hypothesis of independence and homogeneity among errors, we presented a new model considering heterogeneity and dependence among reviewers. Besides, we presented examples with simulate and real data.

Nesta dissertação apresentamos a metodologia de captura-recaptura, sob os enfoques clássico e bayesiano, para estimar o número de erros de um software através de sua inspeção por revisores distintos. Apresentamos o modelo estatístico geral considerando independência entre erros e entre revisores e consideramos os casos particulares de erros igualmente.detectáveis (homogêneos) e revisores não igualmente eficientes (heterogêneos) e de erros não igualmente detectáveis (heterogêneos) e revisores igualmente eficientes (homogêneos). Em seguida, sob a hipótese de heterogeneidade e independência entre erros e homogeneidade e independência entre revisores, supusemos que a heterogeneidade dos erros era expressa por uma classificação destes em fácil e difícil de detectar, admitindo conhecidas as probabilidades de detecção de um erro fácil e de um erro difícil. Finalmente, sob a hipótese de independência e homogeneidade entre erros, apresentamos um novo modelo considerando heterogeneidade e dependência entre revisores. Além disso, apresentamos exemplos com dados simulados e reais.

Advisors/Committee Members: Leite, José Galvão.

Subjects/Keywords: Estatística matemática; Processo seqüêncial de captura-recaptura; MSMC; Inferência bayesiana; Estimativas de máxima verosimilhança; Capture-recapture process; Software review; Maximum likelihood estimates; A priori and a posteriori distributions; Bayes estimates; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA

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APA (6^th Edition):

Silva, K. B. R. d. (2006). Estimativas de máxima verosimilhança e bayesianas do número de erros de um software. (Masters Thesis). Universidade Federal de São Carlos; Programa de Pós-Graduação em Estatística – PPGEs; UFSCar; BR. Retrieved from https://repositorio.ufscar.br/handle/ufscar/4498

Chicago Manual of Style (16^th Edition):

Silva, Karolina Barone Ribeiro da. “Estimativas de máxima verosimilhança e bayesianas do número de erros de um software.” 2006. Masters Thesis, Universidade Federal de São Carlos; Programa de Pós-Graduação em Estatística – PPGEs; UFSCar; BR. Accessed April 12, 2021. https://repositorio.ufscar.br/handle/ufscar/4498.

MLA Handbook (7^th Edition):

Silva, Karolina Barone Ribeiro da. “Estimativas de máxima verosimilhança e bayesianas do número de erros de um software.” 2006. Web. 12 Apr 2021.

Vancouver:

Silva KBRd. Estimativas de máxima verosimilhança e bayesianas do número de erros de um software. [Internet] [Masters thesis]. Universidade Federal de São Carlos; Programa de Pós-Graduação em Estatística – PPGEs; UFSCar; BR; 2006. [cited 2021 Apr 12]. Available from: https://repositorio.ufscar.br/handle/ufscar/4498.

Council of Science Editors:

Silva KBRd. Estimativas de máxima verosimilhança e bayesianas do número de erros de um software. [Masters Thesis]. Universidade Federal de São Carlos; Programa de Pós-Graduação em Estatística – PPGEs; UFSCar; BR; 2006. Available from: https://repositorio.ufscar.br/handle/ufscar/4498

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