Mass-lumping or not mass-lumping for eigenvalue problems
In this article we analyze the effect of mass-lumping in the linear triangular finite element approximation of second-order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass-lumping is always below the one obtained with exact integration. For singular eigenfunctions,...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0749159X_v19_n5_p653_Armentano |
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todo:paper_0749159X_v19_n5_p653_Armentano2023-10-03T15:39:34Z Mass-lumping or not mass-lumping for eigenvalue problems Armentano, M.G. Durán, R.G. Eigenvalue problems Finite elements Mass-lumping In this article we analyze the effect of mass-lumping in the linear triangular finite element approximation of second-order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass-lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass-lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass-lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass-lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0749159X_v19_n5_p653_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 Mass-lumping |
| spellingShingle |
Eigenvalue problems Finite elements Mass-lumping Armentano, M.G. Durán, R.G. Mass-lumping or not mass-lumping for eigenvalue problems |
| topic_facet |
Eigenvalue problems Finite elements Mass-lumping |
| description |
In this article we analyze the effect of mass-lumping in the linear triangular finite element approximation of second-order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass-lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass-lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass-lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass-lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. |
| format |
JOUR |
| author |
Armentano, M.G. Durán, R.G. |
| author_facet |
Armentano, M.G. Durán, R.G. |
| author_sort |
Armentano, M.G. |
| title |
Mass-lumping or not mass-lumping for eigenvalue problems |
| title_short |
Mass-lumping or not mass-lumping for eigenvalue problems |
| title_full |
Mass-lumping or not mass-lumping for eigenvalue problems |
| title_fullStr |
Mass-lumping or not mass-lumping for eigenvalue problems |
| title_full_unstemmed |
Mass-lumping or not mass-lumping for eigenvalue problems |
| title_sort |
mass-lumping or not mass-lumping for eigenvalue problems |
| url |
http://hdl.handle.net/20.500.12110/paper_0749159X_v19_n5_p653_Armentano |
| work_keys_str_mv |
AT armentanomg masslumpingornotmasslumpingforeigenvalueproblems AT duranrg masslumpingornotmasslumpingforeigenvalueproblems |
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1807317984280051712 |