Numerical stochastic homogenization by quasilocal effective diffusion tensors

Dietmar Gallistl; Daniel Peterseim

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arXiv · 1702.08858

Numerical stochastic homogenization by quasilocal effective diffusion tensors

Dietmar Gallistl·Daniel Peterseim

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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.

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Dietmar Gallistl, Daniel Peterseim. 2017-02-28. Numerical stochastic homogenization by quasilocal effective diffusion tensors. https://arxiv.org/abs/1702.08858

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