In this work, we are concerned with the convergence of the multiscale finite element method (MsFEM) for elliptic homogenization problems, where we do not presume 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 $epsilon$ and grid size $H$. 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 (2011)].

@TechReport{Hen11a,
  author       = {Henning, P.},
  title        = {Convergence of MsFEM approximations for elliptic, non-periodic homogenization problems},
  institution  = {FB 10 , Universit\ät M\ünster},
  number       = {04/11 - N},
  month        = {november},
  year         = {2011},
  type         = {Preprint},
  keywords     = {multiscale method, MsFEM, convergence, homogenization},
  url          = \{/2011/Hen11a},
}