Numerical stochastic homogenization by quasilocal effective diffusion tensors

This talk proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales.

The method compresses the random partial differential operator to an effective quasilocal deterministic operator that represents the expected solution on a coarse scale of interest. Error estimates consisting of a priori and a posteriori terms are provided that allow one to quantify the impact of uncertainty in the diffusion coefficient on the expected effective response of the process.