On the asymptotic exactness of error estimators for linear triangular finite elements

Autores
Durán, Ricardo Guillermo; Muschietti, María Amelia; Rodríguez, Rodolfo
Año de publicación
1991
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of elliptic problems. We analyze two estimators based on recovery operators for the gradient of the approximate solution. By using superconvergence results we prove their asymptotic exactness under regularity assumptions on the mesh and the solution. One of the estimators can be easily computed in terms of the jumps of the gradient of the finite element approximation. This estimator is equivalent to the error in the energy norm under rather general conditions. However, we show that for the asymptotic exactness, the regularity assumption on the mesh is not merely technical. While doing this, we analyze the relation between superconvergence and asymptotic exactness for some particular examples.
Facultad de Ciencias Exactas
Materia
Ciencias Exactas
Matemática
elliptic problems
superconvergence
error estimator
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/134060
Acceder
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network_acronym_str SEDICI
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network_name_str SEDICI (UNLP)
spelling On the asymptotic exactness of error estimators for linear triangular finite elementsDurán, Ricardo GuillermoMuschietti, María AmeliaRodríguez, RodolfoCiencias ExactasMatemáticaelliptic problemssuperconvergenceerror estimatorThis paper deals with a-posteriori error estimates for piecewise linear finite element approximations of elliptic problems. We analyze two estimators based on recovery operators for the gradient of the approximate solution. By using superconvergence results we prove their asymptotic exactness under regularity assumptions on the mesh and the solution. One of the estimators can be easily computed in terms of the jumps of the gradient of the finite element approximation. This estimator is equivalent to the error in the energy norm under rather general conditions. However, we show that for the asymptotic exactness, the regularity assumption on the mesh is not merely technical. While doing this, we analyze the relation between superconvergence and asymptotic exactness for some particular examples.Facultad de Ciencias Exactas1991info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf107-127http://sedici.unlp.edu.ar/handle/10915/134060enginfo:eu-repo/semantics/altIdentifier/issn/0029-599xinfo:eu-repo/semantics/altIdentifier/issn/0945-3245info:eu-repo/semantics/altIdentifier/doi/10.1007/bf01385773info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T17:12:42Zoai:sedici.unlp.edu.ar:10915/134060Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 17:12:42.727SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv On the asymptotic exactness of error estimators for linear triangular finite elements
title On the asymptotic exactness of error estimators for linear triangular finite elements
spellingShingle On the asymptotic exactness of error estimators for linear triangular finite elements
Durán, Ricardo Guillermo
Ciencias Exactas
Matemática
elliptic problems
superconvergence
error estimator
title_short On the asymptotic exactness of error estimators for linear triangular finite elements
title_full On the asymptotic exactness of error estimators for linear triangular finite elements
title_fullStr On the asymptotic exactness of error estimators for linear triangular finite elements
title_full_unstemmed On the asymptotic exactness of error estimators for linear triangular finite elements
title_sort On the asymptotic exactness of error estimators for linear triangular finite elements
dc.creator.none.fl_str_mv Durán, Ricardo Guillermo
Muschietti, María Amelia
Rodríguez, Rodolfo
author Durán, Ricardo Guillermo
author_facet Durán, Ricardo Guillermo
Muschietti, María Amelia
Rodríguez, Rodolfo
author_role author
author2 Muschietti, María Amelia
Rodríguez, Rodolfo
author2_role author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Matemática
elliptic problems
superconvergence
error estimator
topic Ciencias Exactas
Matemática
elliptic problems
superconvergence
error estimator
dc.description.none.fl_txt_mv This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of elliptic problems. We analyze two estimators based on recovery operators for the gradient of the approximate solution. By using superconvergence results we prove their asymptotic exactness under regularity assumptions on the mesh and the solution. One of the estimators can be easily computed in terms of the jumps of the gradient of the finite element approximation. This estimator is equivalent to the error in the energy norm under rather general conditions. However, we show that for the asymptotic exactness, the regularity assumption on the mesh is not merely technical. While doing this, we analyze the relation between superconvergence and asymptotic exactness for some particular examples.
Facultad de Ciencias Exactas
description This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of elliptic problems. We analyze two estimators based on recovery operators for the gradient of the approximate solution. By using superconvergence results we prove their asymptotic exactness under regularity assumptions on the mesh and the solution. One of the estimators can be easily computed in terms of the jumps of the gradient of the finite element approximation. This estimator is equivalent to the error in the energy norm under rather general conditions. However, we show that for the asymptotic exactness, the regularity assumption on the mesh is not merely technical. While doing this, we analyze the relation between superconvergence and asymptotic exactness for some particular examples.
publishDate 1991
dc.date.none.fl_str_mv 1991
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/134060
url http://sedici.unlp.edu.ar/handle/10915/134060
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0029-599x
info:eu-repo/semantics/altIdentifier/issn/0945-3245
info:eu-repo/semantics/altIdentifier/doi/10.1007/bf01385773
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
107-127
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 12.982451

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