Finite element approximations in a non-lipschitz domain: part II

Autores
Acosta, Gabriel; Armentano, Maria Gabriela
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In a paper by R. Dur ́ an, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂ R 2 , and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L 2 norm obtaining similar resul ts by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ω h verifies Ω ⊂ Ω h ,inthe above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations.
Fil: Acosta, Gabriel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Armentano, Maria Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Cuspidal Domains
Finite Elements
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:11336/14905
Acceder
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spelling Finite element approximations in a non-lipschitz domain: part IIAcosta, GabrielArmentano, Maria GabrielaCuspidal DomainsFinite ElementsGraded Mesheshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In a paper by R. Dur ́ an, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂ R 2 , and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L 2 norm obtaining similar resul ts by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ω h verifies Ω ⊂ Ω h ,inthe above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations.Fil: Acosta, Gabriel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Armentano, Maria Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAmerican Mathematical Society2011-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14905Acosta, Gabriel; Armentano, Maria Gabriela; Finite element approximations in a non-lipschitz domain: part II; American Mathematical Society; Mathematics Of Computation; 80; 276; 9-2011; 1949-19780025-5718enginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02481-6/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:25:40Zoai:ri.conicet.gov.ar:11336/14905instacron: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:34982025-10-15 14:25:40.816CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Finite element approximations in a non-lipschitz domain: part II
title Finite element approximations in a non-lipschitz domain: part II
spellingShingle Finite element approximations in a non-lipschitz domain: part II
Acosta, Gabriel
Cuspidal Domains
Finite Elements
Graded Meshes
title_short Finite element approximations in a non-lipschitz domain: part II
title_full Finite element approximations in a non-lipschitz domain: part II
title_fullStr Finite element approximations in a non-lipschitz domain: part II
title_full_unstemmed Finite element approximations in a non-lipschitz domain: part II
title_sort Finite element approximations in a non-lipschitz domain: part II
dc.creator.none.fl_str_mv Acosta, Gabriel
Armentano, Maria Gabriela
author Acosta, Gabriel
author_facet Acosta, Gabriel
Armentano, Maria Gabriela
author_role author
author2 Armentano, Maria Gabriela
author2_role author
dc.subject.none.fl_str_mv Cuspidal Domains
Finite Elements
Graded Meshes
topic Cuspidal Domains
Finite Elements
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 a paper by R. Dur ́ an, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂ R 2 , and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L 2 norm obtaining similar resul ts by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ω h verifies Ω ⊂ Ω h ,inthe above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations.
Fil: Acosta, Gabriel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Armentano, Maria Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In a paper by R. Dur ́ an, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂ R 2 , and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L 2 norm obtaining similar resul ts by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ω h verifies Ω ⊂ Ω h ,inthe above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations.
publishDate 2011
dc.date.none.fl_str_mv 2011-09
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/11336/14905
Acosta, Gabriel; Armentano, Maria Gabriela; Finite element approximations in a non-lipschitz domain: part II; American Mathematical Society; Mathematics Of Computation; 80; 276; 9-2011; 1949-1978
0025-5718
url http://hdl.handle.net/11336/14905
identifier_str_mv Acosta, Gabriel; Armentano, Maria Gabriela; Finite element approximations in a non-lipschitz domain: part II; American Mathematical Society; Mathematics Of Computation; 80; 276; 9-2011; 1949-1978
0025-5718
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02481-6/
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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 13.22299

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