Stabilization of low-order cross-grid PkQl mixed finite elements

Autores
Armentano, Maria Gabriela
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we analyze a low-order family of mixed finite element methods for the numerical solution of the Stokes problem and a second order elliptic 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. For the lowest order P1Q0, a global spurious pressure mode is shown to exist and so this element, as P1Q1 case analyzed in Armentano and Blasco (2010), is unstable. However, following the ideas given in Bochev et al. (2006), a simple stabilization procedure can be applied, when we approximate the solution of the Stokes problem, such that the new P1Q0 and P1Q1 methods are unconditionally stable, and achieve optimal accuracy with respect to solution regularity with simple and straightforward implementations. Moreover, we analyze the application of our P1Q1 element to the mixed formulation of the elliptic problem. In this case, by introducing the modified mixed weak form proposed in Brezzi et al. (1993), optimal order of accuracy can be obtained with our stabilized P1Q1 elements. Numerical results are also presented, which confirm the existence of the spurious pressure mode for the P1Q0 element and the excellent stability and accuracy of the new stabilized methods.
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". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
CROSS-GRID ELEMENTS
ELLIPTIC PROBLEMS
MIXED FINITE ELEMENTS
STABILITY ANALYSIS
STOKES PROBLEM
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:11336/88670
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/88670
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Stabilization of low-order cross-grid PkQl mixed finite elementsArmentano, Maria GabrielaCROSS-GRID ELEMENTSELLIPTIC PROBLEMSMIXED FINITE ELEMENTSSTABILITY ANALYSISSTOKES PROBLEMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we analyze a low-order family of mixed finite element methods for the numerical solution of the Stokes problem and a second order elliptic 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. For the lowest order P1Q0, a global spurious pressure mode is shown to exist and so this element, as P1Q1 case analyzed in Armentano and Blasco (2010), is unstable. However, following the ideas given in Bochev et al. (2006), a simple stabilization procedure can be applied, when we approximate the solution of the Stokes problem, such that the new P1Q0 and P1Q1 methods are unconditionally stable, and achieve optimal accuracy with respect to solution regularity with simple and straightforward implementations. Moreover, we analyze the application of our P1Q1 element to the mixed formulation of the elliptic problem. In this case, by introducing the modified mixed weak form proposed in Brezzi et al. (1993), optimal order of accuracy can be obtained with our stabilized P1Q1 elements. Numerical results are also presented, which confirm the existence of the spurious pressure mode for the P1Q0 element and the excellent stability and accuracy of the new stabilized methods.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". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaElsevier Science2018-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/88670Armentano, Maria Gabriela; Stabilization of low-order cross-grid PkQl mixed finite elements; Elsevier Science; Journal Of Computational And Applied Mathematics; 330; 3-2018; 340-3550377-0427CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0377042717304193info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2017.09.002info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:14:06Zoai:ri.conicet.gov.ar:11336/88670instacron: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 10:14:06.308CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stabilization of low-order cross-grid PkQl mixed finite elements
title Stabilization of low-order cross-grid PkQl mixed finite elements
spellingShingle Stabilization of low-order cross-grid PkQl mixed finite elements
Armentano, Maria Gabriela
CROSS-GRID ELEMENTS
ELLIPTIC PROBLEMS
MIXED FINITE ELEMENTS
STABILITY ANALYSIS
STOKES PROBLEM
title_short Stabilization of low-order cross-grid PkQl mixed finite elements
title_full Stabilization of low-order cross-grid PkQl mixed finite elements
title_fullStr Stabilization of low-order cross-grid PkQl mixed finite elements
title_full_unstemmed Stabilization of low-order cross-grid PkQl mixed finite elements
title_sort Stabilization of low-order cross-grid PkQl mixed finite elements
dc.creator.none.fl_str_mv Armentano, Maria Gabriela
author Armentano, Maria Gabriela
author_facet Armentano, Maria Gabriela
author_role author
dc.subject.none.fl_str_mv CROSS-GRID ELEMENTS
ELLIPTIC PROBLEMS
MIXED FINITE ELEMENTS
STABILITY ANALYSIS
STOKES PROBLEM
topic CROSS-GRID ELEMENTS
ELLIPTIC PROBLEMS
MIXED FINITE ELEMENTS
STABILITY ANALYSIS
STOKES 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 In this paper we analyze a low-order family of mixed finite element methods for the numerical solution of the Stokes problem and a second order elliptic 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. For the lowest order P1Q0, a global spurious pressure mode is shown to exist and so this element, as P1Q1 case analyzed in Armentano and Blasco (2010), is unstable. However, following the ideas given in Bochev et al. (2006), a simple stabilization procedure can be applied, when we approximate the solution of the Stokes problem, such that the new P1Q0 and P1Q1 methods are unconditionally stable, and achieve optimal accuracy with respect to solution regularity with simple and straightforward implementations. Moreover, we analyze the application of our P1Q1 element to the mixed formulation of the elliptic problem. In this case, by introducing the modified mixed weak form proposed in Brezzi et al. (1993), optimal order of accuracy can be obtained with our stabilized P1Q1 elements. Numerical results are also presented, which confirm the existence of the spurious pressure mode for the P1Q0 element and the excellent stability and accuracy of the new stabilized methods.
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". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In this paper we analyze a low-order family of mixed finite element methods for the numerical solution of the Stokes problem and a second order elliptic 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. For the lowest order P1Q0, a global spurious pressure mode is shown to exist and so this element, as P1Q1 case analyzed in Armentano and Blasco (2010), is unstable. However, following the ideas given in Bochev et al. (2006), a simple stabilization procedure can be applied, when we approximate the solution of the Stokes problem, such that the new P1Q0 and P1Q1 methods are unconditionally stable, and achieve optimal accuracy with respect to solution regularity with simple and straightforward implementations. Moreover, we analyze the application of our P1Q1 element to the mixed formulation of the elliptic problem. In this case, by introducing the modified mixed weak form proposed in Brezzi et al. (1993), optimal order of accuracy can be obtained with our stabilized P1Q1 elements. Numerical results are also presented, which confirm the existence of the spurious pressure mode for the P1Q0 element and the excellent stability and accuracy of the new stabilized methods.
publishDate 2018
dc.date.none.fl_str_mv 2018-03
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/11336/88670
Armentano, Maria Gabriela; Stabilization of low-order cross-grid PkQl mixed finite elements; Elsevier Science; Journal Of Computational And Applied Mathematics; 330; 3-2018; 340-355
0377-0427
CONICET Digital
CONICET
url http://hdl.handle.net/11336/88670
identifier_str_mv Armentano, Maria Gabriela; Stabilization of low-order cross-grid PkQl mixed finite elements; Elsevier Science; Journal Of Computational And Applied Mathematics; 330; 3-2018; 340-355
0377-0427
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://www.sciencedirect.com/science/article/pii/S0377042717304193
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2017.09.002
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/zip
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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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