Geodesic
A brief introduction to homogenization and miscellaneous applications
Grégoire Allaire1
1 CMAP, Ecole Polytechnique, 91128 Palaiseau, France
ESAIM. Proceedings, Tome 37 (2012), pp. 1-49.

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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.
DOI : 10.1051/proc/201237001

Grégoire Allaire 1

1 CMAP, Ecole Polytechnique, 91128 Palaiseau, France 
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Grégoire Allaire. A brief introduction to homogenization and miscellaneous applications. ESAIM. Proceedings, Tome 37 (2012), pp. 1-49. doi : 10.1051/proc/201237001. http://geodesic.mathdoc.fr/articles/10.1051/proc/201237001/

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