A basic convergence result for conforming adaptive finite element methods

Autores
Morin, Pedro; Siebert, Kunibert G.; Veeser, Andreas
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the approximate solution with adaptive finite elements of a class of linear boundary value problems, which includes problems of "saddle point" type. For the adaptive algorithm we assume the following framework: refinement relies on unique quasi-regular element subdivisions and generates locally quasi-uniform grids, the finite element spaces are conforming, nested, and satisfy the infsup conditions, the error estimator is reliable as well as locally and discretely efficient, and marked elements are subdivided at least once. Under these assumptions, we give a sufficient and essentially necessary condition on marking for the convergence of the finite element solutions to the exact one. This condition is not only satisfied by Dörfler's strategy, but also by the maximum strategy and the equidistribution strategy.
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Siebert, Kunibert G.. Universität Augsburg;
Fil: Veeser, Andreas. Università degli Studi di Milano; Italia
Materia
Adaptivity
Conforming Finite Elements
Adaptivity
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/84102
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/84102
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A basic convergence result for conforming adaptive finite element methodsMorin, PedroSiebert, Kunibert G.Veeser, AndreasAdaptivityConforming Finite ElementsAdaptivityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider the approximate solution with adaptive finite elements of a class of linear boundary value problems, which includes problems of "saddle point" type. For the adaptive algorithm we assume the following framework: refinement relies on unique quasi-regular element subdivisions and generates locally quasi-uniform grids, the finite element spaces are conforming, nested, and satisfy the infsup conditions, the error estimator is reliable as well as locally and discretely efficient, and marked elements are subdivided at least once. Under these assumptions, we give a sufficient and essentially necessary condition on marking for the convergence of the finite element solutions to the exact one. This condition is not only satisfied by Dörfler's strategy, but also by the maximum strategy and the equidistribution strategy.Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Siebert, Kunibert G.. Universität Augsburg;Fil: Veeser, Andreas. Università degli Studi di Milano; ItaliaWorld Scientific2008-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84102Morin, Pedro; Siebert, Kunibert G.; Veeser, Andreas; A basic convergence result for conforming adaptive finite element methods; World Scientific; Mathematical Models And Methods In Applied Sciences; 18; 5; 5-2008; 707-7370218-2025CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202508002838info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:45:15Zoai:ri.conicet.gov.ar:11336/84102instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:45:15.879CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A basic convergence result for conforming adaptive finite element methods
title A basic convergence result for conforming adaptive finite element methods
spellingShingle A basic convergence result for conforming adaptive finite element methods
Morin, Pedro
Adaptivity
Conforming Finite Elements
Adaptivity
title_short A basic convergence result for conforming adaptive finite element methods
title_full A basic convergence result for conforming adaptive finite element methods
title_fullStr A basic convergence result for conforming adaptive finite element methods
title_full_unstemmed A basic convergence result for conforming adaptive finite element methods
title_sort A basic convergence result for conforming adaptive finite element methods
dc.creator.none.fl_str_mv Morin, Pedro
Siebert, Kunibert G.
Veeser, Andreas
author Morin, Pedro
author_facet Morin, Pedro
Siebert, Kunibert G.
Veeser, Andreas
author_role author
author2 Siebert, Kunibert G.
Veeser, Andreas
author2_role author
author
dc.subject.none.fl_str_mv Adaptivity
Conforming Finite Elements
Adaptivity
topic Adaptivity
Conforming Finite Elements
Adaptivity
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider the approximate solution with adaptive finite elements of a class of linear boundary value problems, which includes problems of "saddle point" type. For the adaptive algorithm we assume the following framework: refinement relies on unique quasi-regular element subdivisions and generates locally quasi-uniform grids, the finite element spaces are conforming, nested, and satisfy the infsup conditions, the error estimator is reliable as well as locally and discretely efficient, and marked elements are subdivided at least once. Under these assumptions, we give a sufficient and essentially necessary condition on marking for the convergence of the finite element solutions to the exact one. This condition is not only satisfied by Dörfler's strategy, but also by the maximum strategy and the equidistribution strategy.
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Siebert, Kunibert G.. Universität Augsburg;
Fil: Veeser, Andreas. Università degli Studi di Milano; Italia
description We consider the approximate solution with adaptive finite elements of a class of linear boundary value problems, which includes problems of "saddle point" type. For the adaptive algorithm we assume the following framework: refinement relies on unique quasi-regular element subdivisions and generates locally quasi-uniform grids, the finite element spaces are conforming, nested, and satisfy the infsup conditions, the error estimator is reliable as well as locally and discretely efficient, and marked elements are subdivided at least once. Under these assumptions, we give a sufficient and essentially necessary condition on marking for the convergence of the finite element solutions to the exact one. This condition is not only satisfied by Dörfler's strategy, but also by the maximum strategy and the equidistribution strategy.
publishDate 2008
dc.date.none.fl_str_mv 2008-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/84102
Morin, Pedro; Siebert, Kunibert G.; Veeser, Andreas; A basic convergence result for conforming adaptive finite element methods; World Scientific; Mathematical Models And Methods In Applied Sciences; 18; 5; 5-2008; 707-737
0218-2025
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84102
identifier_str_mv Morin, Pedro; Siebert, Kunibert G.; Veeser, Andreas; A basic convergence result for conforming adaptive finite element methods; World Scientific; Mathematical Models And Methods In Applied Sciences; 18; 5; 5-2008; 707-737
0218-2025
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202508002838
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613421453017088
score 13.070432

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