A unified mixed finite element approximations of the Stokes–Darcy coupled problem

Autores
Armentano, Maria Gabriela; Stockdale, María Lorena
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we develop and analyze a unified approximation of the  velocity-pressure pair for the Stokes-Darcy coupled problem in a plane domain. It is well known that, stable finite element approximations for the Stokes problem may not be appropriate for Darcy problem and for the coupling of fluid flow (modelled by the Stokes equations) with porous media flow (modelled by the Darcyequation), and therefore, different spaces are commonly  used for the discretizations of the Darcy and the Stokes problems. In this work we proposed a modification of the Darcy problem which allows us to apply the classical Mini-element to the whole coupled Stokes-Darcy problem. The proposed method is probably one of the cheapest method for continuous approximation of the coupled system, has optimal accuracy with respect to solution regularity, and has simple and straightforward implementations. Numerical experiments are also presented, which confirm the excellent stability and accuracy of our method.
Fil: Armentano, Maria Gabriela. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Stockdale, María Lorena. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
Stokes-Darcy problem
Mixed finite elements
Stability analysis
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:11336/267825
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/267825
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A unified mixed finite element approximations of the Stokes–Darcy coupled problemArmentano, Maria GabrielaStockdale, María LorenaStokes-Darcy problemMixed finite elementsStability analysishttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we develop and analyze a unified approximation of the  velocity-pressure pair for the Stokes-Darcy coupled problem in a plane domain. It is well known that, stable finite element approximations for the Stokes problem may not be appropriate for Darcy problem and for the coupling of fluid flow (modelled by the Stokes equations) with porous media flow (modelled by the Darcyequation), and therefore, different spaces are commonly  used for the discretizations of the Darcy and the Stokes problems. In this work we proposed a modification of the Darcy problem which allows us to apply the classical Mini-element to the whole coupled Stokes-Darcy problem. The proposed method is probably one of the cheapest method for continuous approximation of the coupled system, has optimal accuracy with respect to solution regularity, and has simple and straightforward implementations. Numerical experiments are also presented, which confirm the excellent stability and accuracy of our method.Fil: Armentano, Maria Gabriela. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Stockdale, María Lorena. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaPergamon-Elsevier Science Ltd2019-05info: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/11336/267825Armentano, Maria Gabriela; Stockdale, María Lorena; A unified mixed finite element approximations of the Stokes–Darcy coupled problem; Pergamon-Elsevier Science Ltd; Computers & Mathematics With Applications (1987); 77; 9; 5-2019; 2568-25840898-1221CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0898122118307302info:eu-repo/semantics/altIdentifier/doi/10.1016/j.camwa.2018.12.032info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:05:47Zoai:ri.conicet.gov.ar:11336/267825instacron: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 10:05:48.283CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A unified mixed finite element approximations of the Stokes–Darcy coupled problem
title A unified mixed finite element approximations of the Stokes–Darcy coupled problem
spellingShingle A unified mixed finite element approximations of the Stokes–Darcy coupled problem
Armentano, Maria Gabriela
Stokes-Darcy problem
Mixed finite elements
Stability analysis
title_short A unified mixed finite element approximations of the Stokes–Darcy coupled problem
title_full A unified mixed finite element approximations of the Stokes–Darcy coupled problem
title_fullStr A unified mixed finite element approximations of the Stokes–Darcy coupled problem
title_full_unstemmed A unified mixed finite element approximations of the Stokes–Darcy coupled problem
title_sort A unified mixed finite element approximations of the Stokes–Darcy coupled problem
dc.creator.none.fl_str_mv Armentano, Maria Gabriela
Stockdale, María Lorena
author Armentano, Maria Gabriela
author_facet Armentano, Maria Gabriela
Stockdale, María Lorena
author_role author
author2 Stockdale, María Lorena
author2_role author
dc.subject.none.fl_str_mv Stokes-Darcy problem
Mixed finite elements
Stability analysis
topic Stokes-Darcy 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 unified approximation of the  velocity-pressure pair for the Stokes-Darcy coupled problem in a plane domain. It is well known that, stable finite element approximations for the Stokes problem may not be appropriate for Darcy problem and for the coupling of fluid flow (modelled by the Stokes equations) with porous media flow (modelled by the Darcyequation), and therefore, different spaces are commonly  used for the discretizations of the Darcy and the Stokes problems. In this work we proposed a modification of the Darcy problem which allows us to apply the classical Mini-element to the whole coupled Stokes-Darcy problem. The proposed method is probably one of the cheapest method for continuous approximation of the coupled system, has optimal accuracy with respect to solution regularity, and has simple and straightforward implementations. Numerical experiments are also presented, which confirm the excellent stability and accuracy of our method.
Fil: Armentano, Maria Gabriela. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Stockdale, María Lorena. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description In this paper we develop and analyze a unified approximation of the  velocity-pressure pair for the Stokes-Darcy coupled problem in a plane domain. It is well known that, stable finite element approximations for the Stokes problem may not be appropriate for Darcy problem and for the coupling of fluid flow (modelled by the Stokes equations) with porous media flow (modelled by the Darcyequation), and therefore, different spaces are commonly  used for the discretizations of the Darcy and the Stokes problems. In this work we proposed a modification of the Darcy problem which allows us to apply the classical Mini-element to the whole coupled Stokes-Darcy problem. The proposed method is probably one of the cheapest method for continuous approximation of the coupled system, has optimal accuracy with respect to solution regularity, and has simple and straightforward implementations. Numerical experiments are also presented, which confirm the excellent stability and accuracy of our method.
publishDate 2019
dc.date.none.fl_str_mv 2019-05
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/11336/267825
Armentano, Maria Gabriela; Stockdale, María Lorena; A unified mixed finite element approximations of the Stokes–Darcy coupled problem; Pergamon-Elsevier Science Ltd; Computers & Mathematics With Applications (1987); 77; 9; 5-2019; 2568-2584
0898-1221
CONICET Digital
CONICET
url http://hdl.handle.net/11336/267825
identifier_str_mv Armentano, Maria Gabriela; Stockdale, María Lorena; A unified mixed finite element approximations of the Stokes–Darcy coupled problem; Pergamon-Elsevier Science Ltd; Computers & Mathematics With Applications (1987); 77; 9; 5-2019; 2568-2584
0898-1221
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/S0898122118307302
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.camwa.2018.12.032
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 Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
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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