Approximation of boundary control problems on curved domains

In this paper we consider boundary control problems associated to a semilinear elliptic equation defined in a curved domain [omega]. The Dirichlet and Neumann cases are analyzed. To deal with the numerical analysis of these problems, the approximation of [omega] by an appropriate domain [omega]h (ty...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Sokolowski, Jan
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/26711
Acceso en línea:https://hdl.handle.net/10902/26711
Access Level:acceso abierto
Palabra clave:Neumann control
Dirichlet control
Curved domains
Error estimates
Semilinearelliptic equations
Second order optimality condition
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spelling Approximation of boundary control problems on curved domainsCasas Rentería, Eduardo|||0000-0002-8364-9416Sokolowski, JanNeumann controlDirichlet controlCurved domainsError estimatesSemilinearelliptic equationsSecond order optimality conditionIn this paper we consider boundary control problems associated to a semilinear elliptic equation defined in a curved domain [omega]. The Dirichlet and Neumann cases are analyzed. To deal with the numerical analysis of these problems, the approximation of [omega] by an appropriate domain [omega]h (typically polygonal) is required. Here we do not consider the numerical approximation of the control problems. Instead, we formulate the corresponding infinite dimensional control problems in [omega]h, and we study the influence of the replacement of [omega] by [omega]h on the solutions of the control problems. Our goal is to compare the optimal controls defined on T=e[omega] with those defined on Th=e[omega]h and to derive some error estimates. The use of a convenient parametrization of the boundary is needed for such estimates.This author was partially supported by the Spanish Ministry of Science and Innovation under projects MTM2008-04206 and “Ingenio Mathematica (i-MATH)” CSD2006-00032 (Consolider Ingenio 2010).Society for Industrial and Applied MathematicsUniversidad de Cantabria20102010-03-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/26711SIAM Journal on Control and Optimization, 2010, 48(6), 3746-3780reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/267112026-06-02T12:39:31Z
dc.title.none.fl_str_mv Approximation of boundary control problems on curved domains
title Approximation of boundary control problems on curved domains
spellingShingle Approximation of boundary control problems on curved domains
Casas Rentería, Eduardo|||0000-0002-8364-9416
Neumann control
Dirichlet control
Curved domains
Error estimates
Semilinearelliptic equations
Second order optimality condition
title_short Approximation of boundary control problems on curved domains
title_full Approximation of boundary control problems on curved domains
title_fullStr Approximation of boundary control problems on curved domains
title_full_unstemmed Approximation of boundary control problems on curved domains
title_sort Approximation of boundary control problems on curved domains
dc.creator.none.fl_str_mv Casas Rentería, Eduardo|||0000-0002-8364-9416
Sokolowski, Jan
author Casas Rentería, Eduardo|||0000-0002-8364-9416
author_facet Casas Rentería, Eduardo|||0000-0002-8364-9416
Sokolowski, Jan
author_role author
author2 Sokolowski, Jan
author2_role author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Neumann control
Dirichlet control
Curved domains
Error estimates
Semilinearelliptic equations
Second order optimality condition
topic Neumann control
Dirichlet control
Curved domains
Error estimates
Semilinearelliptic equations
Second order optimality condition
description In this paper we consider boundary control problems associated to a semilinear elliptic equation defined in a curved domain [omega]. The Dirichlet and Neumann cases are analyzed. To deal with the numerical analysis of these problems, the approximation of [omega] by an appropriate domain [omega]h (typically polygonal) is required. Here we do not consider the numerical approximation of the control problems. Instead, we formulate the corresponding infinite dimensional control problems in [omega]h, and we study the influence of the replacement of [omega] by [omega]h on the solutions of the control problems. Our goal is to compare the optimal controls defined on T=e[omega] with those defined on Th=e[omega]h and to derive some error estimates. The use of a convenient parametrization of the boundary is needed for such estimates.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-03-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/26711
url https://hdl.handle.net/10902/26711
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv SIAM Journal on Control and Optimization, 2010, 48(6), 3746-3780
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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