A posteriori error estimates for non-conforming approximation of eigenvalue problems
We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix-Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the err...
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2012
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v62_n5_p580_Dari http://hdl.handle.net/20.500.12110/paper_01689274_v62_n5_p580_Dari |
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paper:paper_01689274_v62_n5_p580_Dari2023-06-08T15:18:06Z A posteriori error estimates for non-conforming approximation of eigenvalue problems Duran, Ricardo Guillermo Padra, Claudio A posteriori error estimators Eigenvalue problems Non-conforming finite elements A-posteriori error estimates Adaptive procedure Eigen-value Eigenvalue problem Eigenvalues Energy norm Error estimators Higher order terms Laplacians Non-conforming finite elements Nonconforming finite element Number of degrees of freedom Numerical example Posteriori error estimator Three dimensions Upper Bound Error analysis Switching systems Eigenvalues and eigenfunctions We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix-Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the error estimator is equivalent to the energy norm of the eigenvector error up to higher order terms. Moreover, we prove that our estimator provides an upper bound for the error in the approximation of the first eigenvalue, also up to higher order terms. We present numerical examples of an adaptive procedure based on our error estimator in two and three dimensions. These examples show that the error in the adaptive procedure is optimal in terms of the number of degrees of freedom. © 2012 IMACS. Published by Elsevier B.V. All rights reserved. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Padra, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v62_n5_p580_Dari http://hdl.handle.net/20.500.12110/paper_01689274_v62_n5_p580_Dari |
| institution |
Universidad de Buenos Aires |
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I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
A posteriori error estimators Eigenvalue problems Non-conforming finite elements A-posteriori error estimates Adaptive procedure Eigen-value Eigenvalue problem Eigenvalues Energy norm Error estimators Higher order terms Laplacians Non-conforming finite elements Nonconforming finite element Number of degrees of freedom Numerical example Posteriori error estimator Three dimensions Upper Bound Error analysis Switching systems Eigenvalues and eigenfunctions |
| spellingShingle |
A posteriori error estimators Eigenvalue problems Non-conforming finite elements A-posteriori error estimates Adaptive procedure Eigen-value Eigenvalue problem Eigenvalues Energy norm Error estimators Higher order terms Laplacians Non-conforming finite elements Nonconforming finite element Number of degrees of freedom Numerical example Posteriori error estimator Three dimensions Upper Bound Error analysis Switching systems Eigenvalues and eigenfunctions Duran, Ricardo Guillermo Padra, Claudio A posteriori error estimates for non-conforming approximation of eigenvalue problems |
| topic_facet |
A posteriori error estimators Eigenvalue problems Non-conforming finite elements A-posteriori error estimates Adaptive procedure Eigen-value Eigenvalue problem Eigenvalues Energy norm Error estimators Higher order terms Laplacians Non-conforming finite elements Nonconforming finite element Number of degrees of freedom Numerical example Posteriori error estimator Three dimensions Upper Bound Error analysis Switching systems Eigenvalues and eigenfunctions |
| description |
We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix-Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the error estimator is equivalent to the energy norm of the eigenvector error up to higher order terms. Moreover, we prove that our estimator provides an upper bound for the error in the approximation of the first eigenvalue, also up to higher order terms. We present numerical examples of an adaptive procedure based on our error estimator in two and three dimensions. These examples show that the error in the adaptive procedure is optimal in terms of the number of degrees of freedom. © 2012 IMACS. Published by Elsevier B.V. All rights reserved. |
| author |
Duran, Ricardo Guillermo Padra, Claudio |
| author_facet |
Duran, Ricardo Guillermo Padra, Claudio |
| author_sort |
Duran, Ricardo Guillermo |
| title |
A posteriori error estimates for non-conforming approximation of eigenvalue problems |
| title_short |
A posteriori error estimates for non-conforming approximation of eigenvalue problems |
| title_full |
A posteriori error estimates for non-conforming approximation of eigenvalue problems |
| title_fullStr |
A posteriori error estimates for non-conforming approximation of eigenvalue problems |
| title_full_unstemmed |
A posteriori error estimates for non-conforming approximation of eigenvalue problems |
| title_sort |
posteriori error estimates for non-conforming approximation of eigenvalue problems |
| publishDate |
2012 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v62_n5_p580_Dari http://hdl.handle.net/20.500.12110/paper_01689274_v62_n5_p580_Dari |
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1768542500674338816 |