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This paper provides an a~priori error analysis of a localized orthogonaldecomposition method (LOD) for the numerical stochastic homogenization of amodel random diffusion problem. If the uniformly elliptic and bounded randomcoefficient field of the model problem is stationary and satisfies aquantitative decorrelation assumption in form of the spectral gap inequality,then the expected $L^2$ error of the method can be estimated, up to logarithmicfactors, by $H+(\varepsilon/H)^{d/2}$; $\varepsilon$ being the smallcorrelation length of the random coefficient and $H$ the width of the coarsefinite element mesh that determines the spatial resolution. The proof bridgesrecent results of numerical homogenization and quantitative stochastichomogenization.

A priori error analysis of a numerical stochastic homogenization method