Eigenvalue problems in a non-Lipschitz domain

In this paper we analyse piecewise linear finite element approximations of the Laplace eigenvalue problem in the plane domain Ω = (x,y): 0 < x < 1, 0 < y < x, which gives for 1< the simplest model of an external cusp. Since Ω is curved and non-Lipschitz, the classical spectral theory...

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Autores principales: Acosta Rodriguez, Gabriel, Armentano, Maria Gabriela
Publicado: 2014
Materias:
cuspidal domains
eigenvalue problems
finite elements
graded meshes
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v34_n1_p83_Acosta
http://hdl.handle.net/20.500.12110/paper_02724979_v34_n1_p83_Acosta
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_02724979_v34_n1_p83_Acosta2023-06-08T15:25:19Z Eigenvalue problems in a non-Lipschitz domain Acosta Rodriguez, Gabriel Armentano, Maria Gabriela cuspidal domains eigenvalue problems finite elements graded meshes In this paper we analyse piecewise linear finite element approximations of the Laplace eigenvalue problem in the plane domain Ω = (x,y): 0 < x < 1, 0 < y < x, which gives for 1< the simplest model of an external cusp. Since Ω is curved and non-Lipschitz, the classical spectral theory cannot be applied directly. We present the eigenvalue problem in a proper setting, and relying on known convergence results for the associated source problem with <3, we obtain a quasi-optimal order of convergence for the eigenpairs. © 2013 The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. 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. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v34_n1_p83_Acosta http://hdl.handle.net/20.500.12110/paper_02724979_v34_n1_p83_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
eigenvalue problems
finite elements
graded meshes
spellingShingle cuspidal domains
eigenvalue problems
finite elements
graded meshes
Acosta Rodriguez, Gabriel
Armentano, Maria Gabriela
Eigenvalue problems in a non-Lipschitz domain
topic_facet cuspidal domains
eigenvalue problems
finite elements
graded meshes
description In this paper we analyse piecewise linear finite element approximations of the Laplace eigenvalue problem in the plane domain Ω = (x,y): 0 < x < 1, 0 < y < x, which gives for 1< the simplest model of an external cusp. Since Ω is curved and non-Lipschitz, the classical spectral theory cannot be applied directly. We present the eigenvalue problem in a proper setting, and relying on known convergence results for the associated source problem with <3, we obtain a quasi-optimal order of convergence for the eigenpairs. © 2013 The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
author Acosta Rodriguez, Gabriel
Armentano, Maria Gabriela
author_facet Acosta Rodriguez, Gabriel
Armentano, Maria Gabriela
author_sort Acosta Rodriguez, Gabriel
title Eigenvalue problems in a non-Lipschitz domain
title_short Eigenvalue problems in a non-Lipschitz domain
title_full Eigenvalue problems in a non-Lipschitz domain
title_fullStr Eigenvalue problems in a non-Lipschitz domain
title_full_unstemmed Eigenvalue problems in a non-Lipschitz domain
title_sort eigenvalue problems in a non-lipschitz domain
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v34_n1_p83_Acosta
http://hdl.handle.net/20.500.12110/paper_02724979_v34_n1_p83_Acosta
work_keys_str_mv AT acostarodriguezgabriel eigenvalueproblemsinanonlipschitzdomain
AT armentanomariagabriela eigenvalueproblemsinanonlipschitzdomain
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