Asymptotic lower bounds for eigenvalues by nonconforming finite element methods

We analyze the approximation obtained for the eigenvalues of the Laplace operator by the nonconforming piecewise linear finite element of Crouzeix-Raviart. For singular eigenfunctions, as those arising in nonconvex polygons, we prove that the eigenvalues obtained with this method give lower bounds o...

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Autores principales: Armentano, Maria Gabriela, Duran, Ricardo Guillermo
Publicado: 2004
Materias:
Eigenvalue problems
Finite elements
Nonconforming methods
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10689613_v17_n_p93_Armentano
http://hdl.handle.net/20.500.12110/paper_10689613_v17_n_p93_Armentano
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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_10689613_v17_n_p93_Armentano2023-06-08T16:04:22Z Asymptotic lower bounds for eigenvalues by nonconforming finite element methods Armentano, Maria Gabriela Duran, Ricardo Guillermo Eigenvalue problems Finite elements Nonconforming methods We analyze the approximation obtained for the eigenvalues of the Laplace operator by the nonconforming piecewise linear finite element of Crouzeix-Raviart. For singular eigenfunctions, as those arising in nonconvex polygons, we prove that the eigenvalues obtained with this method give lower bounds of the exact eigenvalues when the mesh size is small enough. Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2004 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10689613_v17_n_p93_Armentano http://hdl.handle.net/20.500.12110/paper_10689613_v17_n_p93_Armentano
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Eigenvalue problems
Finite elements
Nonconforming methods
spellingShingle Eigenvalue problems
Finite elements
Nonconforming methods
Armentano, Maria Gabriela
Duran, Ricardo Guillermo
Asymptotic lower bounds for eigenvalues by nonconforming finite element methods
topic_facet Eigenvalue problems
Finite elements
Nonconforming methods
description We analyze the approximation obtained for the eigenvalues of the Laplace operator by the nonconforming piecewise linear finite element of Crouzeix-Raviart. For singular eigenfunctions, as those arising in nonconvex polygons, we prove that the eigenvalues obtained with this method give lower bounds of the exact eigenvalues when the mesh size is small enough.
author Armentano, Maria Gabriela
Duran, Ricardo Guillermo
author_facet Armentano, Maria Gabriela
Duran, Ricardo Guillermo
author_sort Armentano, Maria Gabriela
title Asymptotic lower bounds for eigenvalues by nonconforming finite element methods
title_short Asymptotic lower bounds for eigenvalues by nonconforming finite element methods
title_full Asymptotic lower bounds for eigenvalues by nonconforming finite element methods
title_fullStr Asymptotic lower bounds for eigenvalues by nonconforming finite element methods
title_full_unstemmed Asymptotic lower bounds for eigenvalues by nonconforming finite element methods
title_sort asymptotic lower bounds for eigenvalues by nonconforming finite element methods
publishDate 2004
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10689613_v17_n_p93_Armentano
http://hdl.handle.net/20.500.12110/paper_10689613_v17_n_p93_Armentano
work_keys_str_mv AT armentanomariagabriela asymptoticlowerboundsforeigenvaluesbynonconformingfiniteelementmethods
AT duranricardoguillermo asymptoticlowerboundsforeigenvaluesbynonconformingfiniteelementmethods
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