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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2003
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0749159X_v19_n5_p653_Armentano http://hdl.handle.net/20.500.12110/paper_0749159X_v19_n5_p653_Armentano |
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paper:paper_0749159X_v19_n5_p653_Armentano2023-06-08T15:45:40Z Mass-lumping or not mass-lumping for eigenvalue problems 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. 2003 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0749159X_v19_n5_p653_Armentano 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 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. |
| 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 |
| publishDate |
2003 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0749159X_v19_n5_p653_Armentano http://hdl.handle.net/20.500.12110/paper_0749159X_v19_n5_p653_Armentano |
| _version_ |
1768545423248588800 |