Numerical approximation of a class of problems in stochastic homogenization

In this Note, we study a numerical strategy for the computation of the homogenized matrix for a stochastic elliptic problem that is a small perturbation of a periodic problem. We adapt the analysis introduced in [X. Blanc, C. Le Bris. R-L. Lions. Stochastic homogenization and random lattices, J. Math. Pures Appl. 88 (2007) 34-63] to the case when the corrector problems are numerically solved, and we computationally assess the interest and the accuracy of the approach. (C) 2009 Academie des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.