The first two dayw: basic techniques

In the first day the accent will be on basic ideas, in particular the method of asymptotic expansion and how this can be applied to problems with highly oscillatory characteristics. The aim is to develop effective (upscaled) equations where the oscillations are averaged out, but which are still able to describe the averaged behavior of the system.

The techniques introduced in the first days are further employed in the second day to deal with complex (perforated) domains, such as porous media. Specifically, these idea will be employed for the derivation of the Darcy law and for constructing upscaled models for diffusion, convection, reaction and adsorption in porous media.

Recommended reading:
Homogenization and porous media (Chapters 1 and 6). Edited by Ulrich Hornung. Interdisciplinary Applied Mathematics, 6. Springer-Verlag, New York, 1997.