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arXiv · 1307.0876

An MsFEM type approach for perforated domains

Claude Le Bris·Frederic Legoll·Alexei Lozinski
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Abstract

We follow up on our previous work [C. Le Bris, F. Legoll and A. Lozinski, Chinese Annals of Mathematics 2013] where we have studied a multiscale finite element (MsFEM) type method in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We adapt the approach to address here a multiscale problem on a perforated domain. An additional ingredient of our approach is the enrichment of the multiscale finite element space using bubble functions. We first establish a theoretical error estimate. We next show that, on the problem we consider, the approach we propose outperforms all dedicated existing variants of MsFEM we are aware of.

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Claude Le Bris, Frederic Legoll, Alexei Lozinski. 2013-07-02. An MsFEM type approach for perforated domains. https://arxiv.org/abs/1307.0876

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