Numerical stochastic homogenization by quasilocal effective diffusion tensors
For researchers in numerical homogenization and stochastic PDEs, this provides a rigorous upscaling framework with error control, though it is an incremental extension of existing homogenization techniques.
This paper develops a numerical upscaling method for elliptic problems with random small-scale diffusion tensors, producing a quasilocal effective operator that can be compressed to a PDE. Error estimates quantify the impact of uncertainty on the expected effective response.
This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal discrete integral operator, which can be further compressed to an effective partial differential operator. 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.