A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces

Autores
Agnelli, Juan Pablo; Garau, Eduardo Mario; Morin, Pedro
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article we develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error measured in a weighted Sobolev space. The weight considered is a (positive) power of the distance to the support of the Dirac delta source term, and belongs to the Muckenhoupt’s class A2. The theory hinges on local approximation properties of either Cl´ement or Scott–Zhang interpolation operators, without need of modifications, and makes use of weighted estimates for fractional integrals and maximal functions. Numerical experiments with an adaptive algorithm yield optimal meshes and very good effectivity indices.
Fil: Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional de Córdoba; Argentina
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
Elliptic Problems
Singular Source Term
A Posteriori Error Estimates
Weighted Sobolev Spaces
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:11336/13168
Acceder
id CONICETDig_146ed6aa8fa112ca50e82f3f40da0084
oai_identifier_str oai:ri.conicet.gov.ar:11336/13168
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spacesAgnelli, Juan PabloGarau, Eduardo MarioMorin, PedroElliptic ProblemsSingular Source TermA Posteriori Error EstimatesWeighted Sobolev Spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article we develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error measured in a weighted Sobolev space. The weight considered is a (positive) power of the distance to the support of the Dirac delta source term, and belongs to the Muckenhoupt’s class A2. The theory hinges on local approximation properties of either Cl´ement or Scott–Zhang interpolation operators, without need of modifications, and makes use of weighted estimates for fractional integrals and maximal functions. Numerical experiments with an adaptive algorithm yield optimal meshes and very good effectivity indices.Fil: Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaEdp Sciences2014-02info: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/11336/13168Agnelli, Juan Pablo; Garau, Eduardo Mario; Morin, Pedro; A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces; Edp Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 48; 6; 2-2014; 1557-15810764-583X1290-3841enginfo:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2014010info:eu-repo/semantics/altIdentifier/url/http://www.esaim-m2an.org/articles/m2an/abs/2014/06/m2an140010/m2an140010.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:26:13Zoai:ri.conicet.gov.ar:11336/13168instacron: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 14:26:13.47CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
spellingShingle A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
Agnelli, Juan Pablo
Elliptic Problems
Singular Source Term
A Posteriori Error Estimates
Weighted Sobolev Spaces
title_short A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title_full A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title_fullStr A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title_full_unstemmed A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
title_sort A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
dc.creator.none.fl_str_mv Agnelli, Juan Pablo
Garau, Eduardo Mario
Morin, Pedro
author Agnelli, Juan Pablo
author_facet Agnelli, Juan Pablo
Garau, Eduardo Mario
Morin, Pedro
author_role author
author2 Garau, Eduardo Mario
Morin, Pedro
author2_role author
author
dc.subject.none.fl_str_mv Elliptic Problems
Singular Source Term
A Posteriori Error Estimates
Weighted Sobolev Spaces
topic Elliptic Problems
Singular Source Term
A Posteriori Error Estimates
Weighted Sobolev Spaces
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 develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error measured in a weighted Sobolev space. The weight considered is a (positive) power of the distance to the support of the Dirac delta source term, and belongs to the Muckenhoupt’s class A2. The theory hinges on local approximation properties of either Cl´ement or Scott–Zhang interpolation operators, without need of modifications, and makes use of weighted estimates for fractional integrals and maximal functions. Numerical experiments with an adaptive algorithm yield optimal meshes and very good effectivity indices.
Fil: Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional de Córdoba; Argentina
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description In this article we develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error measured in a weighted Sobolev space. The weight considered is a (positive) power of the distance to the support of the Dirac delta source term, and belongs to the Muckenhoupt’s class A2. The theory hinges on local approximation properties of either Cl´ement or Scott–Zhang interpolation operators, without need of modifications, and makes use of weighted estimates for fractional integrals and maximal functions. Numerical experiments with an adaptive algorithm yield optimal meshes and very good effectivity indices.
publishDate 2014
dc.date.none.fl_str_mv 2014-02
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/11336/13168
Agnelli, Juan Pablo; Garau, Eduardo Mario; Morin, Pedro; A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces; Edp Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 48; 6; 2-2014; 1557-1581
0764-583X
1290-3841
url http://hdl.handle.net/11336/13168
identifier_str_mv Agnelli, Juan Pablo; Garau, Eduardo Mario; Morin, Pedro; A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces; Edp Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 48; 6; 2-2014; 1557-1581
0764-583X
1290-3841
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2014010
info:eu-repo/semantics/altIdentifier/url/http://www.esaim-m2an.org/articles/m2an/abs/2014/06/m2an140010/m2an140010.html
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 Edp Sciences
publisher.none.fl_str_mv Edp Sciences
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
_version_ 1846082704743858176
score 13.22299

Publicaciones similares