# American Institute of Mathematical Sciences

September  2012, 7(3): 503-524. doi: 10.3934/nhm.2012.7.503

## Convergence of MsFEM approximations for elliptic, non-periodic homogenization problems

 1 Institut für Numerische und Angewandte Mathematik, Fachbereich Mathematik und Informatik der Universität Münster, Einsteinstrasse 62, 48149 Münster

Received  November 2011 Revised  May 2012 Published  October 2012

In this work, we are concerned with the convergence of the multiscale finite element method (MsFEM) for elliptic homogenization problems, where we do not assume a certain periodic or stochastic structure, but an averaging assumption which in particular covers periodic and ergodic stochastic coefficients. We also give a result on the convergence in the case of an arbitrary coupling between grid size $H$ and a parameter $\epsilon$. $\epsilon$ is an indicator for the size of the fine scale which converges to zero. The findings of this work are based on the homogenization results obtained in [B. Schweizer and M. Veneroni, The needle problem approach to non-periodic homogenization, Netw. Heterog. Media, 6 (4), 2011].
Citation: Patrick Henning. Convergence of MsFEM approximations for elliptic, non-periodic homogenization problems. Networks & Heterogeneous Media, 2012, 7 (3) : 503-524. doi: 10.3934/nhm.2012.7.503
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