A posteriori error estimation for standard finite element analysis

A new residual type estimator based on projections of the error on subspaces of locally-supported functions is presented. The estimator is defined by a standard element-by-element refinement. First, an approximation of the energy norm of the error is obtained solving local problems with homogeneous...

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Detalhes bibliográficos
Autores: Díez, Pedro|||0000-0001-6464-6407, Egozcue Rubí, Juan José|||0000-0002-5144-4483, Huerta, Antonio|||0000-0003-4198-3798
Formato: artículo
Fecha de publicación:1998
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/8493
Acesso em linha:https://hdl.handle.net/2117/8493
https://dx.doi.org/10.1016/S0045-7825(98)00009-7
Access Level:acceso abierto
Palavra-chave:Finite element method
Error analysis (Mathematics)
Elements finits, Mètode dels
Anàlisi d'error (Matemàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
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network_acronym_str ES
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repository_id_str
spelling A posteriori error estimation for standard finite element analysisDíez, Pedro|||0000-0001-6464-6407Egozcue Rubí, Juan José|||0000-0002-5144-4483Huerta, Antonio|||0000-0003-4198-3798Finite element methodError analysis (Mathematics)Elements finits, Mètode delsAnàlisi d'error (Matemàtica)Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finitsA new residual type estimator based on projections of the error on subspaces of locally-supported functions is presented. The estimator is defined by a standard element-by-element refinement. First, an approximation of the energy norm of the error is obtained solving local problems with homogeneous Dirichlet boundary conditions. A later enrichment of the estimation is performed by adding the contributions of projections on a new family of subspaces. This estimate is a lower bound of the measure of the actual error. The estimator does not need to approximate local boundary conditions for the error equation. Therefore, computation of flux jumps is not necessary. Moreover, the estimator can be applied in mixed meshes containing elements of different shapes and its implementation in a standard finite element code is straightforward. The presented results show the effectiveness of the estimator approximating both the distribution and the global measure of the error, as well as its usefulness in adaptive procedures.Peer Reviewed19981998-09-0120102010-07-30journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/8493https://dx.doi.org/10.1016/S0045-7825(98)00009-7reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/84932026-05-27T15:37:01Z
dc.title.none.fl_str_mv A posteriori error estimation for standard finite element analysis
title A posteriori error estimation for standard finite element analysis
spellingShingle A posteriori error estimation for standard finite element analysis
Díez, Pedro|||0000-0001-6464-6407
Finite element method
Error analysis (Mathematics)
Elements finits, Mètode dels
Anàlisi d'error (Matemàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
title_short A posteriori error estimation for standard finite element analysis
title_full A posteriori error estimation for standard finite element analysis
title_fullStr A posteriori error estimation for standard finite element analysis
title_full_unstemmed A posteriori error estimation for standard finite element analysis
title_sort A posteriori error estimation for standard finite element analysis
dc.creator.none.fl_str_mv Díez, Pedro|||0000-0001-6464-6407
Egozcue Rubí, Juan José|||0000-0002-5144-4483
Huerta, Antonio|||0000-0003-4198-3798
author Díez, Pedro|||0000-0001-6464-6407
author_facet Díez, Pedro|||0000-0001-6464-6407
Egozcue Rubí, Juan José|||0000-0002-5144-4483
Huerta, Antonio|||0000-0003-4198-3798
author_role author
author2 Egozcue Rubí, Juan José|||0000-0002-5144-4483
Huerta, Antonio|||0000-0003-4198-3798
author2_role author
author
dc.subject.none.fl_str_mv Finite element method
Error analysis (Mathematics)
Elements finits, Mètode dels
Anàlisi d'error (Matemàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
topic Finite element method
Error analysis (Mathematics)
Elements finits, Mètode dels
Anàlisi d'error (Matemàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
description A new residual type estimator based on projections of the error on subspaces of locally-supported functions is presented. The estimator is defined by a standard element-by-element refinement. First, an approximation of the energy norm of the error is obtained solving local problems with homogeneous Dirichlet boundary conditions. A later enrichment of the estimation is performed by adding the contributions of projections on a new family of subspaces. This estimate is a lower bound of the measure of the actual error. The estimator does not need to approximate local boundary conditions for the error equation. Therefore, computation of flux jumps is not necessary. Moreover, the estimator can be applied in mixed meshes containing elements of different shapes and its implementation in a standard finite element code is straightforward. The presented results show the effectiveness of the estimator approximating both the distribution and the global measure of the error, as well as its usefulness in adaptive procedures.
publishDate 1998
dc.date.none.fl_str_mv 1998
1998-09-01
2010
2010-07-30
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/8493
https://dx.doi.org/10.1016/S0045-7825(98)00009-7
url https://hdl.handle.net/2117/8493
https://dx.doi.org/10.1016/S0045-7825(98)00009-7
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.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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