An introduction to asymptotic homogenization

Abstract

We present an introduction to the asymptotic homogenization technique as a follow up of the four hours course held at the International Workshop on Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization, and Applications (M3TB2015) at TU Darmstadt (Germany) on 28 September 2015. The content is well-known, although revisited to provide a first insight to scientists and (especially) students who are unaware of the topic. We present the technique via three simple and instructive examples (one-dimensional and multi-dimensional diffusion and the Stokes’s problem for porous media) remarking on the role of regularity assumptions (periodicity vs. local boundedness) and non-dimensionalization, which are sometimes not sufficiently clarified in the existing literature.