A priori error analysis of a numerical stochastic homogenization method

12/25/2019

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by   J. Fischer, et al.

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