A Priori Error Analysis of a Numerical Stochastic Homogenization Method

This paper provides an a priori error analysis of localized orthogonal decomposition method for the numerical stochastic homogenization model random diffusion problem. If uniformly elliptic and bounded coefficient field problem is stationary satisfies quantitative decorrelation assumption in form spectral gap inequality, then expected $L^2$ can be estimated, up to logarithmic factors, by $H+(\varepsilon/H)^{d/2}$, $\varepsilon$ being small correlation length $H$ width coarse finite element mesh that determines spatial resolution. The proof bridges recent results homogenization.