An MsFEM type approach for perforated domains

Claude Le Bris (1, 2) , Frédéric Legoll (3, 1) , Alexei Lozinski (4, 5)

1 MATHERIALS - MATHematics for MatERIALS
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes
4 IMT - Institut de Mathématiques de Toulouse UMR5219
5 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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.

Domaines: Analyse numérique [math.NA]

Claude Le Bris, Frédéric Legoll, Alexei Lozinski. An MsFEM type approach for perforated domains. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2014, 12 (3), pp.1046-1077. ⟨10.1137/130927826⟩. ⟨hal-00841308⟩