We address multiscale elliptic problems with random coefficients that are a perturbationof multiscale deterministic problems. Our approach consists in taking benefit of theperturbative context to suitably modify the classical Finite Element basis into adeterministic multiscale Finite Element basis. The latter essentially shares the sameapproximation properties as a multiscale Finite Element basis directly generated on therandom problem. The specific reference method that we use is the Multiscale Finite ElementMethod. Using numerical experiments, we demonstrate the efficiency of our approach and thecomputational speed-up with respect to a more standard approach. In the stationarysetting, we provide a complete analysis of the approach, extending that available for thedeterministic periodic setting.
