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
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00255718_v80_n276_p1949_Acosta_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_00255718_v80_n276_p1949_Acosta_oai
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spelling	I28-R145-paper_00255718_v80_n276_p1949_Acosta_oai2024-08-16 Acosta, G. Armentano, M.G. 2011 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00255718_v80_n276_p1949_Acosta info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Math. Comput. 2011;80(276):1949-1978 Cuspidal domains Finite elements Graded meshes Finite element approximations in a non-Lipschitz domain: Part II info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00255718_v80_n276_p1949_Acosta_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00255718_v80_n276_p1949_Acosta_oai
work_keys_str_mv	AT acostag finiteelementapproximationsinanonlipschitzdomainpartii AT armentanomg finiteelementapproximationsinanonlipschitzdomainpartii
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Finite element approximations in a non-Lipschitz domain: Part II

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