Rocky Mountain Journal of Mathematics

Expository Paper: A primer on homogenization of elliptic PDEs with stationary and ergodic random coefficient functions

Alen Alexanderian

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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.

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Rocky Mountain J. Math., Volume 45, Number 3 (2015), 703-735.

First available in Project Euclid: 21 August 2015

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Zentralblatt MATH identifier

Primary: 37A05: Measure-preserving transformations 37A25: Ergodicity, mixing, rates of mixing 78A48: Composite media; random media 78M40: Homogenization

Homogenization random media ergodic dynamical system stationary random field diffusion in random media


Alexanderian, Alen. Expository Paper: A primer on homogenization of elliptic PDEs with stationary and ergodic random coefficient functions. Rocky Mountain J. Math. 45 (2015), no. 3, 703--735. doi:10.1216/RMJ-2015-45-3-703.

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