Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources

Autores
Ojea, Ignacio
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the problem -Δu=f, where f has a point-singularity. In particular, we are interested in f = δx0, a Dirac delta with support in x0, but singularities of the form f|x - x0|-s are also considered. We prove the stability of the Galerkin projection on graded meshes in weighted spaces, with weights given by powers of the distance to x0. We also recover optimal rates of convergence for the finite element method on these graded meshes. Our approach is general and holds both in two and three dimensions. Numerical experiments are shown that verify our results, and lead to interesting observations.
Fil: Ojea, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
A PRIORI ERROR ESTIMATES
FINITE ELEMENTS
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:11336/164931
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sourcesOjea, IgnacioA PRIORI ERROR ESTIMATESFINITE ELEMENTSWEIGHTED SOBOLEV SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the problem -Δu=f, where f has a point-singularity. In particular, we are interested in f = δx0, a Dirac delta with support in x0, but singularities of the form f|x - x0|-s are also considered. We prove the stability of the Galerkin projection on graded meshes in weighted spaces, with weights given by powers of the distance to x0. We also recover optimal rates of convergence for the finite element method on these graded meshes. Our approach is general and holds both in two and three dimensions. Numerical experiments are shown that verify our results, and lead to interesting observations.Fil: Ojea, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaEDP Sciences2021-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/164931Ojea, Ignacio; Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 55; 8-2021; S879-S9070764-583X2804-7214CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2020065info:eu-repo/semantics/altIdentifier/url/https://www.esaim-m2an.org/articles/m2an/abs/2021/01/m2an190167/m2an190167.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 Técnicas2025-09-03T09:53:59Zoai:ri.conicet.gov.ar:11336/164931instacron: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:34982025-09-03 09:54:01.19CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources
title Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources
spellingShingle Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources
Ojea, Ignacio
A PRIORI ERROR ESTIMATES
FINITE ELEMENTS
WEIGHTED SOBOLEV SPACES
title_short Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources
title_full Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources
title_fullStr Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources
title_full_unstemmed Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources
title_sort Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources
dc.creator.none.fl_str_mv Ojea, Ignacio
author Ojea, Ignacio
author_facet Ojea, Ignacio
author_role author
dc.subject.none.fl_str_mv A PRIORI ERROR ESTIMATES
FINITE ELEMENTS
WEIGHTED SOBOLEV SPACES
topic A PRIORI ERROR ESTIMATES
FINITE ELEMENTS
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 We study the problem -Δu=f, where f has a point-singularity. In particular, we are interested in f = δx0, a Dirac delta with support in x0, but singularities of the form f|x - x0|-s are also considered. We prove the stability of the Galerkin projection on graded meshes in weighted spaces, with weights given by powers of the distance to x0. We also recover optimal rates of convergence for the finite element method on these graded meshes. Our approach is general and holds both in two and three dimensions. Numerical experiments are shown that verify our results, and lead to interesting observations.
Fil: Ojea, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We study the problem -Δu=f, where f has a point-singularity. In particular, we are interested in f = δx0, a Dirac delta with support in x0, but singularities of the form f|x - x0|-s are also considered. We prove the stability of the Galerkin projection on graded meshes in weighted spaces, with weights given by powers of the distance to x0. We also recover optimal rates of convergence for the finite element method on these graded meshes. Our approach is general and holds both in two and three dimensions. Numerical experiments are shown that verify our results, and lead to interesting observations.
publishDate 2021
dc.date.none.fl_str_mv 2021-08
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/11336/164931
Ojea, Ignacio; Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 55; 8-2021; S879-S907
0764-583X
2804-7214
CONICET Digital
CONICET
url http://hdl.handle.net/11336/164931
identifier_str_mv Ojea, Ignacio; Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 55; 8-2021; S879-S907
0764-583X
2804-7214
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2020065
info:eu-repo/semantics/altIdentifier/url/https://www.esaim-m2an.org/articles/m2an/abs/2021/01/m2an190167/m2an190167.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
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_ 1842269260206833664
score 13.13397

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