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

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 Rodriguez, Gabriel, Armentano, Maria Gabriela
Publicado: 2011
Materias:
Cuspidal domains
Finite elements
Graded meshes
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v80_n276_p1949_Acosta
http://hdl.handle.net/20.500.12110/paper_00255718_v80_n276_p1949_Acosta
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00255718_v80_n276_p1949_Acosta
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spelling paper:paper_00255718_v80_n276_p1949_Acosta2023-06-08T14:53:16Z Finite element approximations in a non-Lipschitz domain: Part II Acosta Rodriguez, Gabriel Armentano, Maria Gabriela 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v80_n276_p1949_Acosta 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)
topic Cuspidal domains
Finite elements
Graded meshes
spellingShingle Cuspidal domains
Finite elements
Graded meshes
Acosta Rodriguez, Gabriel
Armentano, Maria Gabriela
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.
author Acosta Rodriguez, Gabriel
Armentano, Maria Gabriela
author_facet Acosta Rodriguez, Gabriel
Armentano, Maria Gabriela
author_sort Acosta Rodriguez, Gabriel
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v80_n276_p1949_Acosta
http://hdl.handle.net/20.500.12110/paper_00255718_v80_n276_p1949_Acosta
work_keys_str_mv AT acostarodriguezgabriel finiteelementapproximationsinanonlipschitzdomainpartii
AT armentanomariagabriela finiteelementapproximationsinanonlipschitzdomainpartii
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