A brief introduction to homogenization and miscellaneous applications*

Allaire, Grégoire. Cancès, E., and Labbé, S., eds. " A brief introduction to homogenization and miscellaneous applications*." ESAIM: Proceedings 37 (2012): 1-49. <http://eudml.org/doc/251234>.

@article{Allaire2012,
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.},
author = {Allaire, Grégoire},
editor = {Cancès, E., Labbé, S.},
journal = {ESAIM: Proceedings},
keywords = {two-scale asymptotic expansion; G-convergence; H-convergence; Darcy's law},
language = {eng},
month = {9},
pages = {1-49},
publisher = {EDP Sciences},
title = { A brief introduction to homogenization and miscellaneous applications*},
url = {http://eudml.org/doc/251234},
volume = {37},
year = {2012},
}

TY - JOUR
AU - Allaire, Grégoire
AU - Cancès, E.
AU - Labbé, S.
TI - A brief introduction to homogenization and miscellaneous applications*
JO - ESAIM: Proceedings
DA - 2012/9//
PB - EDP Sciences
VL - 37
SP - 1
EP - 49
AB - 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.
LA - eng
KW - two-scale asymptotic expansion; G-convergence; H-convergence; Darcy's law
UR - http://eudml.org/doc/251234
ER -