Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)

Autores
Apel, Thomas; Lombardi, Ariel Luis; Winkler, Max
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the singular behaviour of the solution in the vicinity of the non-smooth parts of the boundary. The discretization error is analyzed for the piecewise linear approximation in the H1(Ω)- and L2(Ω)-norms by using a new quasi-interpolation operator. This new interpolant is introduced in order to prove the estimates for L2(Ω)-data in the differential equation which is not possible for the standard nodal interpolant. These new estimates allow for the extension of certain error estimates for optimal control problems with elliptic partial differential equations and for a simpler proof of the discrete compactness property for edge elements of any order on this kind of finite element meshes.
Fil: Apel, Thomas. Universität der Bundeswehr München; Alemania
Fil: Lombardi, Ariel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Universidad de Buenos Aires; Argentina
Fil: Winkler, Max. Universität der Bundeswehr München; Alemania
Materia
Finite Element Method
Edfe And Corner Singularities
Anisotropic Mesh Grading
Elliptic Boundary Value Problem
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:11336/35857
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/35857
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)Apel, ThomasLombardi, Ariel LuisWinkler, MaxFinite Element MethodEdfe And Corner SingularitiesAnisotropic Mesh GradingElliptic Boundary Value Problemhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the singular behaviour of the solution in the vicinity of the non-smooth parts of the boundary. The discretization error is analyzed for the piecewise linear approximation in the H1(Ω)- and L2(Ω)-norms by using a new quasi-interpolation operator. This new interpolant is introduced in order to prove the estimates for L2(Ω)-data in the differential equation which is not possible for the standard nodal interpolant. These new estimates allow for the extension of certain error estimates for optimal control problems with elliptic partial differential equations and for a simpler proof of the discrete compactness property for edge elements of any order on this kind of finite element meshes.Fil: Apel, Thomas. Universität der Bundeswehr München; AlemaniaFil: Lombardi, Ariel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Universidad de Buenos Aires; ArgentinaFil: Winkler, Max. Universität der Bundeswehr München; AlemaniaEDP Sciences2014-08info: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/11336/35857Apel, Thomas; Lombardi, Ariel Luis; Winkler, Max; Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω); EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 48; 4; 8-2014; 1117-11450764-583XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1303.2960.pdfinfo:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2013134info:eu-repo/semantics/altIdentifier/url/https://www.esaim-m2an.org/articles/m2an/abs/2014/04/m2an130134/m2an130134.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 Técnicas2025-09-03T09:53:25Zoai:ri.conicet.gov.ar:11336/35857instacron: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 09:53:25.905CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)
title Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)
spellingShingle Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)
Apel, Thomas
Finite Element Method
Edfe And Corner Singularities
Anisotropic Mesh Grading
Elliptic Boundary Value Problem
title_short Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)
title_full Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)
title_fullStr Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)
title_full_unstemmed Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)
title_sort Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω)
dc.creator.none.fl_str_mv Apel, Thomas
Lombardi, Ariel Luis
Winkler, Max
author Apel, Thomas
author_facet Apel, Thomas
Lombardi, Ariel Luis
Winkler, Max
author_role author
author2 Lombardi, Ariel Luis
Winkler, Max
author2_role author
author
dc.subject.none.fl_str_mv Finite Element Method
Edfe And Corner Singularities
Anisotropic Mesh Grading
Elliptic Boundary Value Problem
topic Finite Element Method
Edfe And Corner Singularities
Anisotropic Mesh Grading
Elliptic Boundary Value Problem
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the singular behaviour of the solution in the vicinity of the non-smooth parts of the boundary. The discretization error is analyzed for the piecewise linear approximation in the H1(Ω)- and L2(Ω)-norms by using a new quasi-interpolation operator. This new interpolant is introduced in order to prove the estimates for L2(Ω)-data in the differential equation which is not possible for the standard nodal interpolant. These new estimates allow for the extension of certain error estimates for optimal control problems with elliptic partial differential equations and for a simpler proof of the discrete compactness property for edge elements of any order on this kind of finite element meshes.
Fil: Apel, Thomas. Universität der Bundeswehr München; Alemania
Fil: Lombardi, Ariel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Universidad de Buenos Aires; Argentina
Fil: Winkler, Max. Universität der Bundeswehr München; Alemania
description The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the singular behaviour of the solution in the vicinity of the non-smooth parts of the boundary. The discretization error is analyzed for the piecewise linear approximation in the H1(Ω)- and L2(Ω)-norms by using a new quasi-interpolation operator. This new interpolant is introduced in order to prove the estimates for L2(Ω)-data in the differential equation which is not possible for the standard nodal interpolant. These new estimates allow for the extension of certain error estimates for optimal control problems with elliptic partial differential equations and for a simpler proof of the discrete compactness property for edge elements of any order on this kind of finite element meshes.
publishDate 2014
dc.date.none.fl_str_mv 2014-08
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/11336/35857
Apel, Thomas; Lombardi, Ariel Luis; Winkler, Max; Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω); EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 48; 4; 8-2014; 1117-1145
0764-583X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/35857
identifier_str_mv Apel, Thomas; Lombardi, Ariel Luis; Winkler, Max; Anisotropic mesh refinement in polyhedral domains: error estimates with data in L 2 (Ω); EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 48; 4; 8-2014; 1117-1145
0764-583X
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://arxiv.org/pdf/1303.2960.pdf
info:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2013134
info:eu-repo/semantics/altIdentifier/url/https://www.esaim-m2an.org/articles/m2an/abs/2014/04/m2an130134/m2an130134.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
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score 13.13397

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