Finite element approximations in a non-Lipschitz domain: Part II
- Autores
- Acosta, G.; Armentano, M.G.
- Año de publicación
- 2011
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In a paper by R. Durán, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂R{double struck}2, and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L2 norm obtaining similar results by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ωh verifies Ω ⊂ Ωh, in the above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations. © 2011 American Mathematical Society.
Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. - Fuente
- Math. Comput. 2011;80(276):1949-1978
- Materia
-
Cuspidal domains
Finite elements
Graded meshes - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/2.5/ar
- Repositorio
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_00255718_v80_n276_p1949_Acosta
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Finite element approximations in a non-Lipschitz domain: Part IIAcosta, G.Armentano, M.G.Cuspidal domainsFinite elementsGraded meshesIn a paper by R. Durán, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂R{double struck}2, and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L2 norm obtaining similar results by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ωh verifies Ω ⊂ Ωh, in the above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations. © 2011 American Mathematical Society.Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00255718_v80_n276_p1949_AcostaMath. Comput. 2011;80(276):1949-1978reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:43:09Zpaperaa:paper_00255718_v80_n276_p1949_AcostaInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:43:10.662Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
dc.title.none.fl_str_mv |
Finite element approximations in a non-Lipschitz domain: Part II |
title |
Finite element approximations in a non-Lipschitz domain: Part II |
spellingShingle |
Finite element approximations in a non-Lipschitz domain: Part II Acosta, G. Cuspidal domains Finite elements Graded meshes |
title_short |
Finite element approximations in a non-Lipschitz domain: Part II |
title_full |
Finite element approximations in a non-Lipschitz domain: Part II |
title_fullStr |
Finite element approximations in a non-Lipschitz domain: Part II |
title_full_unstemmed |
Finite element approximations in a non-Lipschitz domain: Part II |
title_sort |
Finite element approximations in a non-Lipschitz domain: Part II |
dc.creator.none.fl_str_mv |
Acosta, G. Armentano, M.G. |
author |
Acosta, G. |
author_facet |
Acosta, G. Armentano, M.G. |
author_role |
author |
author2 |
Armentano, M.G. |
author2_role |
author |
dc.subject.none.fl_str_mv |
Cuspidal domains Finite elements Graded meshes |
topic |
Cuspidal domains Finite elements Graded meshes |
dc.description.none.fl_txt_mv |
In a paper by R. Durán, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂R{double struck}2, and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L2 norm obtaining similar results by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ωh verifies Ω ⊂ Ωh, in the above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations. © 2011 American Mathematical Society. Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. |
description |
In a paper by R. Durán, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂R{double struck}2, and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L2 norm obtaining similar results by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ωh verifies Ω ⊂ Ωh, in the above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations. © 2011 American Mathematical Society. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011 |
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/20.500.12110/paper_00255718_v80_n276_p1949_Acosta |
url |
http://hdl.handle.net/20.500.12110/paper_00255718_v80_n276_p1949_Acosta |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar |
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openAccess |
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http://creativecommons.org/licenses/by/2.5/ar |
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application/pdf |
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Math. Comput. 2011;80(276):1949-1978 reponame:Biblioteca Digital (UBA-FCEN) instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales instacron:UBA-FCEN |
reponame_str |
Biblioteca Digital (UBA-FCEN) |
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Biblioteca Digital (UBA-FCEN) |
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Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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UBA-FCEN |
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Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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ana@bl.fcen.uba.ar |
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