Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian

Autores
del Pezzo, Leandro Martin; Lombardi, Ariel Luis; Martinez, Sandra Rita
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we construct an “interior penalty” discontinuous Galerkin method to approximate the minimizer of a variational problem related to the $p(x)$-Laplacian. The function $p:\Omega\to [p_1,p_2]$ is log-Hölder continuous and $1Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lombardi, Ariel Luis. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Martinez, Sandra Rita. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Variable exponent spaces
Minimization
Discontinuous Galerkin
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:11336/19994
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19994
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplaciandel Pezzo, Leandro MartinLombardi, Ariel LuisMartinez, Sandra RitaVariable exponent spacesMinimizationDiscontinuous Galerkinhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we construct an “interior penalty” discontinuous Galerkin method to approximate the minimizer of a variational problem related to the $p(x)$-Laplacian. The function $p:\Omega\to [p_1,p_2]$ is log-Hölder continuous and $1<p_1\leq p_2<\infty$. We prove that the minimizers of the discrete functional converge to the solution. We also make some numerical experiments in dimension one to compare this method with the conforming Galerkin method, in the case where $p_1$ is close to one. This example is motivated by its applications to image processing.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lombardi, Ariel Luis. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Martinez, Sandra Rita. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSiam Publications2012-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19994del Pezzo, Leandro Martin; Lombardi, Ariel Luis; Martinez, Sandra Rita; Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian; Siam Publications; Siam Journal On Numerical Analysis; 50; 5; 9-2012; 2497-25210036-14291095-7170CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1137/110820324info:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/abs/10.1137/110820324info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:42:12Zoai:ri.conicet.gov.ar:11336/19994instacron: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 10:42:12.461CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian
title Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian
spellingShingle Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian
del Pezzo, Leandro Martin
Variable exponent spaces
Minimization
Discontinuous Galerkin
title_short Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian
title_full Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian
title_fullStr Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian
title_full_unstemmed Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian
title_sort Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian
dc.creator.none.fl_str_mv del Pezzo, Leandro Martin
Lombardi, Ariel Luis
Martinez, Sandra Rita
author del Pezzo, Leandro Martin
author_facet del Pezzo, Leandro Martin
Lombardi, Ariel Luis
Martinez, Sandra Rita
author_role author
author2 Lombardi, Ariel Luis
Martinez, Sandra Rita
author2_role author
author
dc.subject.none.fl_str_mv Variable exponent spaces
Minimization
Discontinuous Galerkin
topic Variable exponent spaces
Minimization
Discontinuous Galerkin
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 construct an “interior penalty” discontinuous Galerkin method to approximate the minimizer of a variational problem related to the $p(x)$-Laplacian. The function $p:\Omega\to [p_1,p_2]$ is log-Hölder continuous and $1<p_1\leq p_2<\infty$. We prove that the minimizers of the discrete functional converge to the solution. We also make some numerical experiments in dimension one to compare this method with the conforming Galerkin method, in the case where $p_1$ is close to one. This example is motivated by its applications to image processing.
Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lombardi, Ariel Luis. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Martinez, Sandra Rita. 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 construct an “interior penalty” discontinuous Galerkin method to approximate the minimizer of a variational problem related to the $p(x)$-Laplacian. The function $p:\Omega\to [p_1,p_2]$ is log-Hölder continuous and $1<p_1\leq p_2<\infty$. We prove that the minimizers of the discrete functional converge to the solution. We also make some numerical experiments in dimension one to compare this method with the conforming Galerkin method, in the case where $p_1$ is close to one. This example is motivated by its applications to image processing.
publishDate 2012
dc.date.none.fl_str_mv 2012-09
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/11336/19994
del Pezzo, Leandro Martin; Lombardi, Ariel Luis; Martinez, Sandra Rita; Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian; Siam Publications; Siam Journal On Numerical Analysis; 50; 5; 9-2012; 2497-2521
0036-1429
1095-7170
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19994
identifier_str_mv del Pezzo, Leandro Martin; Lombardi, Ariel Luis; Martinez, Sandra Rita; Interior penalty discontinuous Galerkin FEM for the $p(x)$-Laplacian; Siam Publications; Siam Journal On Numerical Analysis; 50; 5; 9-2012; 2497-2521
0036-1429
1095-7170
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1137/110820324
info:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/abs/10.1137/110820324
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
dc.publisher.none.fl_str_mv Siam Publications
publisher.none.fl_str_mv Siam Publications
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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