A Primer on Homogenization of Elliptic PDEs with Stationary and Ergodic Random Coefficient Functions

Abstract

We study the problem of characterizing the effective (homogenized) properties of materials whose diffusive properties are modeled with random fields. Focusing on elliptic PDEs with stationary and ergodic random coefficient functions, we provide a gentle introduction to the mathematical theory of homogenization of random media. We also present numerical examples to elucidate the theoretical concepts and results.

23 pages; corrected some minor typos; to appear in Rocky Mountain Journal of Mathematics

References in corpus (2)

• Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity
• Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited

Cited by in corpus (1)

• Physics-informed neural networks for learning the homogenized coefficients of multiscale elliptic equations