Analysis of finite element approximations of stokes equations with nonsmooth data
- Autores
- Duran, Ricardo Guillermo; Gastaldi, Lucia; Lombardi, Ariel Luis
- Año de publicación
- 2020
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we analyze the finite element approximation of the Stokes equations with nonsmooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard finite element method to the regularized problem. We prove almost optimal order error estimates for two regularization procedures in the case of general data in fractional order Sobolev spaces and for the Lagrange interpolation (with appropriate modifications at the discontinuities) for piecewise smooth data. Our results apply in particular to the classic lid-driven cavity problem, improving the error estimates obtained in Cai and Wang [Math. Comp., 78 (2009), pp. 771-787]. Finally, we introduce and analyze an a posteriori error estimator. We prove its reliability and efficiency and show some numerical examples which suggest that optimal order of convergence is obtained by an adaptive procedure based on our estimator.
Fil: Duran, Ricardo Guillermo. 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
Fil: Gastaldi, Lucia. Università degli Studi di Brescia; Italia
Fil: Lombardi, Ariel Luis. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina - Materia
-
A POSTERIORI ERROR ANALYSIS
FINITE ELEMENTS
NONSMOOTH DATA
STOKES EQUATIONS - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/151105
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Analysis of finite element approximations of stokes equations with nonsmooth dataDuran, Ricardo GuillermoGastaldi, LuciaLombardi, Ariel LuisA POSTERIORI ERROR ANALYSISFINITE ELEMENTSNONSMOOTH DATASTOKES EQUATIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we analyze the finite element approximation of the Stokes equations with nonsmooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard finite element method to the regularized problem. We prove almost optimal order error estimates for two regularization procedures in the case of general data in fractional order Sobolev spaces and for the Lagrange interpolation (with appropriate modifications at the discontinuities) for piecewise smooth data. Our results apply in particular to the classic lid-driven cavity problem, improving the error estimates obtained in Cai and Wang [Math. Comp., 78 (2009), pp. 771-787]. Finally, we introduce and analyze an a posteriori error estimator. We prove its reliability and efficiency and show some numerical examples which suggest that optimal order of convergence is obtained by an adaptive procedure based on our estimator.Fil: Duran, Ricardo Guillermo. 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"; ArgentinaFil: Gastaldi, Lucia. Università degli Studi di Brescia; ItaliaFil: Lombardi, Ariel Luis. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaSociety for Industrial and Applied Mathematics2020-11-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/151105Duran, Ricardo Guillermo; Gastaldi, Lucia; Lombardi, Ariel Luis; Analysis of finite element approximations of stokes equations with nonsmooth data; Society for Industrial and Applied Mathematics; Siam Journal on Numerical Analysis; 58; 6; 12-11-2020; 3309-33310036-14291095-7170CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://epubs.siam.org/doi/10.1137/19M1305872info:eu-repo/semantics/altIdentifier/doi/10.1137/19M1305872info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1912.04962info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:39:18Zoai:ri.conicet.gov.ar:11336/151105instacron: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 09:39:19.099CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Analysis of finite element approximations of stokes equations with nonsmooth data |
title |
Analysis of finite element approximations of stokes equations with nonsmooth data |
spellingShingle |
Analysis of finite element approximations of stokes equations with nonsmooth data Duran, Ricardo Guillermo A POSTERIORI ERROR ANALYSIS FINITE ELEMENTS NONSMOOTH DATA STOKES EQUATIONS |
title_short |
Analysis of finite element approximations of stokes equations with nonsmooth data |
title_full |
Analysis of finite element approximations of stokes equations with nonsmooth data |
title_fullStr |
Analysis of finite element approximations of stokes equations with nonsmooth data |
title_full_unstemmed |
Analysis of finite element approximations of stokes equations with nonsmooth data |
title_sort |
Analysis of finite element approximations of stokes equations with nonsmooth data |
dc.creator.none.fl_str_mv |
Duran, Ricardo Guillermo Gastaldi, Lucia Lombardi, Ariel Luis |
author |
Duran, Ricardo Guillermo |
author_facet |
Duran, Ricardo Guillermo Gastaldi, Lucia Lombardi, Ariel Luis |
author_role |
author |
author2 |
Gastaldi, Lucia Lombardi, Ariel Luis |
author2_role |
author author |
dc.subject.none.fl_str_mv |
A POSTERIORI ERROR ANALYSIS FINITE ELEMENTS NONSMOOTH DATA STOKES EQUATIONS |
topic |
A POSTERIORI ERROR ANALYSIS FINITE ELEMENTS NONSMOOTH DATA STOKES EQUATIONS |
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 the finite element approximation of the Stokes equations with nonsmooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard finite element method to the regularized problem. We prove almost optimal order error estimates for two regularization procedures in the case of general data in fractional order Sobolev spaces and for the Lagrange interpolation (with appropriate modifications at the discontinuities) for piecewise smooth data. Our results apply in particular to the classic lid-driven cavity problem, improving the error estimates obtained in Cai and Wang [Math. Comp., 78 (2009), pp. 771-787]. Finally, we introduce and analyze an a posteriori error estimator. We prove its reliability and efficiency and show some numerical examples which suggest that optimal order of convergence is obtained by an adaptive procedure based on our estimator. Fil: Duran, Ricardo Guillermo. 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 Fil: Gastaldi, Lucia. Università degli Studi di Brescia; Italia Fil: Lombardi, Ariel Luis. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina |
description |
In this paper we analyze the finite element approximation of the Stokes equations with nonsmooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard finite element method to the regularized problem. We prove almost optimal order error estimates for two regularization procedures in the case of general data in fractional order Sobolev spaces and for the Lagrange interpolation (with appropriate modifications at the discontinuities) for piecewise smooth data. Our results apply in particular to the classic lid-driven cavity problem, improving the error estimates obtained in Cai and Wang [Math. Comp., 78 (2009), pp. 771-787]. Finally, we introduce and analyze an a posteriori error estimator. We prove its reliability and efficiency and show some numerical examples which suggest that optimal order of convergence is obtained by an adaptive procedure based on our estimator. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-11-12 |
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/11336/151105 Duran, Ricardo Guillermo; Gastaldi, Lucia; Lombardi, Ariel Luis; Analysis of finite element approximations of stokes equations with nonsmooth data; Society for Industrial and Applied Mathematics; Siam Journal on Numerical Analysis; 58; 6; 12-11-2020; 3309-3331 0036-1429 1095-7170 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/151105 |
identifier_str_mv |
Duran, Ricardo Guillermo; Gastaldi, Lucia; Lombardi, Ariel Luis; Analysis of finite element approximations of stokes equations with nonsmooth data; Society for Industrial and Applied Mathematics; Siam Journal on Numerical Analysis; 58; 6; 12-11-2020; 3309-3331 0036-1429 1095-7170 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://epubs.siam.org/doi/10.1137/19M1305872 info:eu-repo/semantics/altIdentifier/doi/10.1137/19M1305872 info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1912.04962 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by/2.5/ar/ |
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application/pdf application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics |
publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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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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