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.
@article{arxiv.1307.0876,
title = {An MsFEM type approach for perforated domains},
author = {Claude Le Bris and Frederic Legoll and Alexei Lozinski},
journal= {arXiv preprint arXiv:1307.0876},
year = {2013}
}