Finite element approximations in a non-Lipschitz domain: Part II

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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 stud...

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Autores principales: Acosta, G., Armentano, M.G.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2011
Materias:
Cuspidal domains
Finite elements
Graded meshes
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00255718_v80_n276_p1949_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_00255718_v80_n276_p1949_Acosta
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spelling paperaa:paper_00255718_v80_n276_p1949_Acosta2023-06-12T16:45:08Z Finite element approximations in a non-Lipschitz domain: Part II Math. Comput. 2011;80(276):1949-1978 Acosta, G. Armentano, M.G. Cuspidal domains Finite elements Graded meshes 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. 2011 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00255718_v80_n276_p1949_Acosta
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Cuspidal domains
Finite elements
Graded meshes
spellingShingle Cuspidal domains
Finite elements
Graded meshes
Acosta, G.
Armentano, M.G.
Finite element approximations in a non-Lipschitz domain: Part II
topic_facet Cuspidal domains
Finite elements
Graded meshes
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.
format Artículo
Artículo
publishedVersion
author Acosta, G.
Armentano, M.G.
author_facet Acosta, G.
Armentano, M.G.
author_sort Acosta, G.
title Finite element approximations in a non-Lipschitz domain: Part II
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
publishDate 2011
url http://hdl.handle.net/20.500.12110/paper_00255718_v80_n276_p1949_Acosta
work_keys_str_mv AT acostag finiteelementapproximationsinanonlipschitzdomainpartii
AT armentanomg finiteelementapproximationsinanonlipschitzdomainpartii
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