Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem

Autores
Armentano, Maria Gabriela; Blasco, Jordi
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we develop and analyze a family of mixed finite element methods for the numerical solution of the Stokes problem in two space dimensions. In these schemes, the pressure is interpolated on a mesh of rectangular elements, while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals. Continuous interpolations of degrees k for the velocity and l for the pressure are considered, so the new finite elements are called cross-grid PkQl. A stability analysis of these approximations is provided, based on the macroelement technique of Stenberg. The lowest order P1Q1 and P2Q1 cases are analyzed in detail; in the first case, a global spurious pressure mode is shown to exist, so this element is unstable. In the second case, however, stability is rigorously proved. Numerical results obtained in these two cases are also presented, which confirm the existence of the spurious pressure mode for the P1Q1 element and the stability of the P2Q1 element.
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
Fil: Blasco, Jordi. Universidad Politecnica de Catalunya; España
Materia
Stokes Problem
Mixed Finite Elements
Stability Analysis
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15024
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problemArmentano, Maria GabrielaBlasco, JordiStokes ProblemMixed Finite ElementsStability Analysishttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we develop and analyze a family of mixed finite element methods for the numerical solution of the Stokes problem in two space dimensions. In these schemes, the pressure is interpolated on a mesh of rectangular elements, while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals. Continuous interpolations of degrees k for the velocity and l for the pressure are considered, so the new finite elements are called cross-grid PkQl. A stability analysis of these approximations is provided, based on the macroelement technique of Stenberg. The lowest order P1Q1 and P2Q1 cases are analyzed in detail; in the first case, a global spurious pressure mode is shown to exist, so this element is unstable. In the second case, however, stability is rigorously proved. Numerical results obtained in these two cases are also presented, which confirm the existence of the spurious pressure mode for the P1Q1 element and the stability of the P2Q1 element.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"; ArgentinaFil: Blasco, Jordi. Universidad Politecnica de Catalunya; EspañaElsevier2010-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15024Armentano, Maria Gabriela; Blasco, Jordi; Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem; Elsevier; Journal Of Computational And Applied Mathematics; 234; 5; 7-2010; 1404-14160377-0427enginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0377042710000981info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2010.02.016info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:23:27Zoai:ri.conicet.gov.ar:11336/15024instacron: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 10:23:27.833CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem
title Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem
spellingShingle Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem
Armentano, Maria Gabriela
Stokes Problem
Mixed Finite Elements
Stability Analysis
title_short Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem
title_full Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem
title_fullStr Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem
title_full_unstemmed Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem
title_sort Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem
dc.creator.none.fl_str_mv Armentano, Maria Gabriela
Blasco, Jordi
author Armentano, Maria Gabriela
author_facet Armentano, Maria Gabriela
Blasco, Jordi
author_role author
author2 Blasco, Jordi
author2_role author
dc.subject.none.fl_str_mv Stokes Problem
Mixed Finite Elements
Stability Analysis
topic Stokes Problem
Mixed Finite Elements
Stability Analysis
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 develop and analyze a family of mixed finite element methods for the numerical solution of the Stokes problem in two space dimensions. In these schemes, the pressure is interpolated on a mesh of rectangular elements, while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals. Continuous interpolations of degrees k for the velocity and l for the pressure are considered, so the new finite elements are called cross-grid PkQl. A stability analysis of these approximations is provided, based on the macroelement technique of Stenberg. The lowest order P1Q1 and P2Q1 cases are analyzed in detail; in the first case, a global spurious pressure mode is shown to exist, so this element is unstable. In the second case, however, stability is rigorously proved. Numerical results obtained in these two cases are also presented, which confirm the existence of the spurious pressure mode for the P1Q1 element and the stability of the P2Q1 element.
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
Fil: Blasco, Jordi. Universidad Politecnica de Catalunya; España
description In this paper we develop and analyze a family of mixed finite element methods for the numerical solution of the Stokes problem in two space dimensions. In these schemes, the pressure is interpolated on a mesh of rectangular elements, while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals. Continuous interpolations of degrees k for the velocity and l for the pressure are considered, so the new finite elements are called cross-grid PkQl. A stability analysis of these approximations is provided, based on the macroelement technique of Stenberg. The lowest order P1Q1 and P2Q1 cases are analyzed in detail; in the first case, a global spurious pressure mode is shown to exist, so this element is unstable. In the second case, however, stability is rigorously proved. Numerical results obtained in these two cases are also presented, which confirm the existence of the spurious pressure mode for the P1Q1 element and the stability of the P2Q1 element.
publishDate 2010
dc.date.none.fl_str_mv 2010-07
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/11336/15024
Armentano, Maria Gabriela; Blasco, Jordi; Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem; Elsevier; Journal Of Computational And Applied Mathematics; 234; 5; 7-2010; 1404-1416
0377-0427
url http://hdl.handle.net/11336/15024
identifier_str_mv Armentano, Maria Gabriela; Blasco, Jordi; Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem; Elsevier; Journal Of Computational And Applied Mathematics; 234; 5; 7-2010; 1404-1416
0377-0427
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0377042710000981
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2010.02.016
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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