Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes

Autores
Durán, Rodrigo Gonzalo; Lombardi, Ariel Luis; Prieto, Mariana Ines
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we analyse the approximation of a model convection-diffusion equation by standard bilinear finite elements using the graded meshes introduced in Durán & Lombardi (2006, Finite element approximation of convection-diffusion problems using graded meshes. Appl. Numer. Math., 56, 1314-1325). Our main goal is to prove superconvergence results of the type known for standard elliptic problems, namely, that the difference between the finite element solution and the Lagrange interpolation of the exact solution, in the ε-weighted H 1-norm, is of higher order than the error itself. The constant in our estimate depends only weakly on the singular perturbation parameter. As a consequence of the superconvergence result we obtain optimal order error estimates in the L 2-norm. Also we show how to obtain a higher order approximation by a local postprocessing of the computed solution.
Fil: Durán, Rodrigo Gonzalo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Lombardi, Ariel Luis. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Prieto, Mariana Ines. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
CONVECTION-DIFFUSION
GRADED MESHES
SUPERCONVERGENCE
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:11336/113340
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Superconvergence for finite element approximation of a convection-diffusion equation using graded meshesDurán, Rodrigo GonzaloLombardi, Ariel LuisPrieto, Mariana InesCONVECTION-DIFFUSIONGRADED MESHESSUPERCONVERGENCEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we analyse the approximation of a model convection-diffusion equation by standard bilinear finite elements using the graded meshes introduced in Durán & Lombardi (2006, Finite element approximation of convection-diffusion problems using graded meshes. Appl. Numer. Math., 56, 1314-1325). Our main goal is to prove superconvergence results of the type known for standard elliptic problems, namely, that the difference between the finite element solution and the Lagrange interpolation of the exact solution, in the ε-weighted H 1-norm, is of higher order than the error itself. The constant in our estimate depends only weakly on the singular perturbation parameter. As a consequence of the superconvergence result we obtain optimal order error estimates in the L 2-norm. Also we show how to obtain a higher order approximation by a local postprocessing of the computed solution.Fil: Durán, Rodrigo Gonzalo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Lombardi, Ariel Luis. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Prieto, Mariana Ines. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaOxford University Press2012-04info: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/11336/113340Durán, Rodrigo Gonzalo; Lombardi, Ariel Luis; Prieto, Mariana Ines; Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes; Oxford University Press; Ima Journal Of Numerical Analysis; 32; 2; 4-2012; 511-5330272-4979CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imajna/article-abstract/32/2/511/752114?redirectedFrom=fulltextinfo:eu-repo/semantics/altIdentifier/doi/10.1093/imanum/drr005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:02:38Zoai:ri.conicet.gov.ar:11336/113340instacron: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 11:02:38.613CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
spellingShingle Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
Durán, Rodrigo Gonzalo
CONVECTION-DIFFUSION
GRADED MESHES
SUPERCONVERGENCE
title_short Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title_full Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title_fullStr Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title_full_unstemmed Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title_sort Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
dc.creator.none.fl_str_mv Durán, Rodrigo Gonzalo
Lombardi, Ariel Luis
Prieto, Mariana Ines
author Durán, Rodrigo Gonzalo
author_facet Durán, Rodrigo Gonzalo
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 CONVECTION-DIFFUSION
GRADED MESHES
SUPERCONVERGENCE
topic CONVECTION-DIFFUSION
GRADED MESHES
SUPERCONVERGENCE
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 analyse the approximation of a model convection-diffusion equation by standard bilinear finite elements using the graded meshes introduced in Durán & Lombardi (2006, Finite element approximation of convection-diffusion problems using graded meshes. Appl. Numer. Math., 56, 1314-1325). Our main goal is to prove superconvergence results of the type known for standard elliptic problems, namely, that the difference between the finite element solution and the Lagrange interpolation of the exact solution, in the ε-weighted H 1-norm, is of higher order than the error itself. The constant in our estimate depends only weakly on the singular perturbation parameter. As a consequence of the superconvergence result we obtain optimal order error estimates in the L 2-norm. Also we show how to obtain a higher order approximation by a local postprocessing of the computed solution.
Fil: Durán, Rodrigo Gonzalo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Lombardi, Ariel Luis. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Prieto, Mariana Ines. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description In this paper we analyse the approximation of a model convection-diffusion equation by standard bilinear finite elements using the graded meshes introduced in Durán & Lombardi (2006, Finite element approximation of convection-diffusion problems using graded meshes. Appl. Numer. Math., 56, 1314-1325). Our main goal is to prove superconvergence results of the type known for standard elliptic problems, namely, that the difference between the finite element solution and the Lagrange interpolation of the exact solution, in the ε-weighted H 1-norm, is of higher order than the error itself. The constant in our estimate depends only weakly on the singular perturbation parameter. As a consequence of the superconvergence result we obtain optimal order error estimates in the L 2-norm. Also we show how to obtain a higher order approximation by a local postprocessing of the computed solution.
publishDate 2012
dc.date.none.fl_str_mv 2012-04
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/11336/113340
Durán, Rodrigo Gonzalo; Lombardi, Ariel Luis; Prieto, Mariana Ines; Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes; Oxford University Press; Ima Journal Of Numerical Analysis; 32; 2; 4-2012; 511-533
0272-4979
CONICET Digital
CONICET
url http://hdl.handle.net/11336/113340
identifier_str_mv Durán, Rodrigo Gonzalo; Lombardi, Ariel Luis; Prieto, Mariana Ines; Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes; Oxford University Press; Ima Journal Of Numerical Analysis; 32; 2; 4-2012; 511-533
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/32/2/511/752114?redirectedFrom=fulltext
info:eu-repo/semantics/altIdentifier/doi/10.1093/imanum/drr005
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 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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