Convergence rates for adaptive finite elements

Autores
Gaspoz, Fernando Daniel; Morin, Pedro
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article, we prove that it is possible to construct, using newest vertex bisection, meshes that equidistribute the error in the H1-norm whenever the function to be approximated can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of partial differential equations. As a consequence, the meshes turn out to be quasi-optimal, and convergence rates for adaptive finite-element methods using Lagrange finite elements of any polynomial degree are obtained.
Fil: Gaspoz, Fernando Daniel. 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: Morin, Pedro. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
ADAPTIVE FINITE ELEMENTS
CONVERGENCE RATES
OPTIMALITY
REGULARITY
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:11336/186275
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Convergence rates for adaptive finite elementsGaspoz, Fernando DanielMorin, PedroADAPTIVE FINITE ELEMENTSCONVERGENCE RATESOPTIMALITYREGULARITYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article, we prove that it is possible to construct, using newest vertex bisection, meshes that equidistribute the error in the H1-norm whenever the function to be approximated can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of partial differential equations. As a consequence, the meshes turn out to be quasi-optimal, and convergence rates for adaptive finite-element methods using Lagrange finite elements of any polynomial degree are obtained.Fil: Gaspoz, Fernando Daniel. 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: Morin, Pedro. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaOxford University Press2008-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/186275Gaspoz, Fernando Daniel; Morin, Pedro; Convergence rates for adaptive finite elements; Oxford University Press; Ima Journal Of Numerical Analysis; 29; 4; 12-2008; 917-9360272-4979CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imajna/article-abstract/29/4/917/671423info:eu-repo/semantics/altIdentifier/doi/10.1093/imanum/drn039info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:05:21Zoai:ri.conicet.gov.ar:11336/186275instacron: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:34982025-10-22 12:05:22.171CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Convergence rates for adaptive finite elements
title Convergence rates for adaptive finite elements
spellingShingle Convergence rates for adaptive finite elements
Gaspoz, Fernando Daniel
ADAPTIVE FINITE ELEMENTS
CONVERGENCE RATES
OPTIMALITY
REGULARITY
title_short Convergence rates for adaptive finite elements
title_full Convergence rates for adaptive finite elements
title_fullStr Convergence rates for adaptive finite elements
title_full_unstemmed Convergence rates for adaptive finite elements
title_sort Convergence rates for adaptive finite elements
dc.creator.none.fl_str_mv Gaspoz, Fernando Daniel
Morin, Pedro
author Gaspoz, Fernando Daniel
author_facet Gaspoz, Fernando Daniel
Morin, Pedro
author_role author
author2 Morin, Pedro
author2_role author
dc.subject.none.fl_str_mv ADAPTIVE FINITE ELEMENTS
CONVERGENCE RATES
OPTIMALITY
REGULARITY
topic ADAPTIVE FINITE ELEMENTS
CONVERGENCE RATES
OPTIMALITY
REGULARITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this article, we prove that it is possible to construct, using newest vertex bisection, meshes that equidistribute the error in the H1-norm whenever the function to be approximated can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of partial differential equations. As a consequence, the meshes turn out to be quasi-optimal, and convergence rates for adaptive finite-element methods using Lagrange finite elements of any polynomial degree are obtained.
Fil: Gaspoz, Fernando Daniel. 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: Morin, Pedro. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this article, we prove that it is possible to construct, using newest vertex bisection, meshes that equidistribute the error in the H1-norm whenever the function to be approximated can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of partial differential equations. As a consequence, the meshes turn out to be quasi-optimal, and convergence rates for adaptive finite-element methods using Lagrange finite elements of any polynomial degree are obtained.
publishDate 2008
dc.date.none.fl_str_mv 2008-12
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/11336/186275
Gaspoz, Fernando Daniel; Morin, Pedro; Convergence rates for adaptive finite elements; Oxford University Press; Ima Journal Of Numerical Analysis; 29; 4; 12-2008; 917-936
0272-4979
CONICET Digital
CONICET
url http://hdl.handle.net/11336/186275
identifier_str_mv Gaspoz, Fernando Daniel; Morin, Pedro; Convergence rates for adaptive finite elements; Oxford University Press; Ima Journal Of Numerical Analysis; 29; 4; 12-2008; 917-936
0272-4979
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imajna/article-abstract/29/4/917/671423
info:eu-repo/semantics/altIdentifier/doi/10.1093/imanum/drn039
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
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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
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score 12.982451

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