A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems

This paper deals with a posteriori error estimators for the non conforming CrouzeixRaviart finite element approximations of the Steklov eigenvalue problem. First, we define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove the equivalen...

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Detalles Bibliográficos
Autores principales: Dello Russo, Anahí, Alonso, Ana Esther
Formato: Articulo
Lenguaje:Inglés
Publicado: 2011
Materias:
Matemática
A posteriori error estimates
Nonconforming finite element methods
Steklov eigenvalue problem
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/84137
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-84137
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
A posteriori error estimates
Nonconforming finite element methods
Steklov eigenvalue problem
spellingShingle Matemática
A posteriori error estimates
Nonconforming finite element methods
Steklov eigenvalue problem
Dello Russo, Anahí
Alonso, Ana Esther
A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems
topic_facet Matemática
A posteriori error estimates
Nonconforming finite element methods
Steklov eigenvalue problem
description This paper deals with a posteriori error estimators for the non conforming CrouzeixRaviart finite element approximations of the Steklov eigenvalue problem. First, we define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove the equivalence between this estimator and the broken energy norm of the error with constants independent of the corresponding eigenvalue. Next, we prove that edge residuals dominate the volumetric part of the residual and that the volumetric part of the residual terms dominate the normal component of the jumps of the discrete fluxes across interior edges. Finally, based on these results, we introduce two simpler equivalent error estimators. The analysis shows that these a posteriori error estimates are optimal up to higher order terms and that may be used for the design of adaptive algorithms.
format Articulo
Articulo
author Dello Russo, Anahí
Alonso, Ana Esther
author_facet Dello Russo, Anahí
Alonso, Ana Esther
author_sort Dello Russo, Anahí
title A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems
title_short A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems
title_full A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems
title_fullStr A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems
title_full_unstemmed A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems
title_sort posteriori error estimates for nonconforming approximations of steklov eigenvalue problems
publishDate 2011
url http://sedici.unlp.edu.ar/handle/10915/84137
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AT dellorussoanahi posteriorierrorestimatesfornonconformingapproximationsofstekloveigenvalueproblems
AT alonsoanaesther posteriorierrorestimatesfornonconformingapproximationsofstekloveigenvalueproblems
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