Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation

Autores
Duran, Ricardo Guillermo; Lombardi, Ariel Luis; Prieto, Mariana Ines
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we analyze the standard piece-wise bilinear finite element approximation of a model reaction–diffusion problem. We prove supercloseness results when appropriate graded meshes are used. The meshes are those introduced in Durán and Lombardi (2005) [8] but with a stronger restriction on the graduation parameter. As a consequence we obtain almost optimal error estimates in the L 2 -norm thus completing the error analysis given in Durán and Lombardi (2005).
Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Lombardi, Ariel Luis. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento; Argentina
Fil: Prieto, Mariana Ines. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Finite Elements
Supercloseness
Superconvergence
Graded Meshes
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:11336/18804
Acceder
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spelling Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equationDuran, Ricardo GuillermoLombardi, Ariel LuisPrieto, Mariana InesFinite ElementsSuperclosenessSuperconvergenceGraded Mesheshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we analyze the standard piece-wise bilinear finite element approximation of a model reaction–diffusion problem. We prove supercloseness results when appropriate graded meshes are used. The meshes are those introduced in Durán and Lombardi (2005) [8] but with a stronger restriction on the graduation parameter. As a consequence we obtain almost optimal error estimates in the L 2 -norm thus completing the error analysis given in Durán and Lombardi (2005).Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Lombardi, Ariel Luis. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento; ArgentinaFil: Prieto, Mariana Ines. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2013-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18804Duran, Ricardo Guillermo; Lombardi, Ariel Luis; Prieto, Mariana Ines; Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation; Elsevier Science; Journal Of Computational And Applied Mathematics; 242; 4-2013; 232-2470377-0427CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2012.10.004info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0377042712004232info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:38:32Zoai:ri.conicet.gov.ar:11336/18804instacron: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 09:38:32.393CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation
title Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation
spellingShingle Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation
Duran, Ricardo Guillermo
Finite Elements
Supercloseness
Superconvergence
Graded Meshes
title_short Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation
title_full Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation
title_fullStr Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation
title_full_unstemmed Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation
title_sort Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation
dc.creator.none.fl_str_mv Duran, Ricardo Guillermo
Lombardi, Ariel Luis
Prieto, Mariana Ines
author Duran, Ricardo Guillermo
author_facet Duran, Ricardo Guillermo
Lombardi, Ariel Luis
Prieto, Mariana Ines
author_role author
author2 Lombardi, Ariel Luis
Prieto, Mariana Ines
author2_role author
author
dc.subject.none.fl_str_mv Finite Elements
Supercloseness
Superconvergence
Graded Meshes
topic Finite Elements
Supercloseness
Superconvergence
Graded Meshes
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 paper we analyze the standard piece-wise bilinear finite element approximation of a model reaction–diffusion problem. We prove supercloseness results when appropriate graded meshes are used. The meshes are those introduced in Durán and Lombardi (2005) [8] but with a stronger restriction on the graduation parameter. As a consequence we obtain almost optimal error estimates in the L 2 -norm thus completing the error analysis given in Durán and Lombardi (2005).
Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Lombardi, Ariel Luis. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento; Argentina
Fil: Prieto, Mariana Ines. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this paper we analyze the standard piece-wise bilinear finite element approximation of a model reaction–diffusion problem. We prove supercloseness results when appropriate graded meshes are used. The meshes are those introduced in Durán and Lombardi (2005) [8] but with a stronger restriction on the graduation parameter. As a consequence we obtain almost optimal error estimates in the L 2 -norm thus completing the error analysis given in Durán and Lombardi (2005).
publishDate 2013
dc.date.none.fl_str_mv 2013-04
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/11336/18804
Duran, Ricardo Guillermo; Lombardi, Ariel Luis; Prieto, Mariana Ines; Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation; Elsevier Science; Journal Of Computational And Applied Mathematics; 242; 4-2013; 232-247
0377-0427
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18804
identifier_str_mv Duran, Ricardo Guillermo; Lombardi, Ariel Luis; Prieto, Mariana Ines; Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation; Elsevier Science; Journal Of Computational And Applied Mathematics; 242; 4-2013; 232-247
0377-0427
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2012.10.004
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0377042712004232
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
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 13.070432

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