Oversampling for the Multiscale Finite Element Method
This paper reviews standard oversampling strategies as performed in the multiscale finite element method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch including coarse finite element functions. We suggest, by contrast, performing lo...
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Published in | Multiscale modeling & simulation Vol. 11; no. 4; pp. 1149 - 1175 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2013
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Subjects | |
Online Access | Get full text |
ISSN | 1540-3459 1540-3467 1540-3467 |
DOI | 10.1137/120900332 |
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Summary: | This paper reviews standard oversampling strategies as performed in the multiscale finite element method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch including coarse finite element functions. We suggest, by contrast, performing local computations with the additional constraint that trial and test functions be linear independent from coarse finite element functions. This approach reinterprets the variational multiscale method in the context of computational homogenization. This connection gives rise to a general fully discrete error analysis for the proposed multiscale method with constrained oversampling without any resonance effects. In particular, we are able to give the first rigorous proof of convergence for an MsFEM with oversampling. [PUBLICATION ABSTRACT] |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
ISSN: | 1540-3459 1540-3467 1540-3467 |
DOI: | 10.1137/120900332 |