Numerical stochastic homogenization by quasilocal effective diffusion tensors
Numerical Analysis
2019-01-24 v2
Abstract
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.
Cite
@article{arxiv.1702.08858,
title = {Numerical stochastic homogenization by quasilocal effective diffusion tensors},
author = {Dietmar Gallistl and Daniel Peterseim},
journal= {arXiv preprint arXiv:1702.08858},
year = {2019}
}