A brief introduction to homogenization and miscellaneous applications

Abstract

This paper is a set of lecture notes for a short introductory course on homogenization. It covers the basic tools of periodic homogenization (two-scale asymptotic expansions, the oscillating test function method and two-scale convergence) and briefly describes the main results of the more general theory of G− or H−convergence. Several applications of the method are given: derivation of Darcy’s law for flows in porous media, derivation of the porosity model and long time behavior of a diffusion equation. Numerical agorithms for homogenization are also discussed, including multiscale finite element methods.