0100046 – Analytical and Numerical Homogenization

The objective of this lecture is to give an introduction to multiscale problems and (some) analytical and numerical homogenization techniques. Since a lot of research work has been dedicated to the field in recent years, not all aspects can be covered within this lecture. Nevertheless, the goal is to become familiar with general questions and ideas in the field of (elliptic) multiscale problems and corresponding methods. Specifically, we will cover: (i) a one-dimensional introduction to the overall questions and problems related to multiscale problems and homogenization (ii) general concepts of convergence (iii) the Heterogeneous Multiscale Method (iv) the Localized Orthogonal Decomposition method. Some (basic) knowledge on finite element methods and functional analysis is helpful for the lecture but not required.