Homogenizace eliptických rovnic

Abstract

In this thesis we study mathematical homogenization of elliptic equations for heterogeneous materials with fine periodic structure. Both ordinary and partial differential equations were studied and for both cases we state and prove homogenization theorems. Two-scale convergence method that reflects behaviour of rapidly oscillating functions is introduced for proof of homogenization theorem in N dimensions. We also present an overview of practical implementation for solving homogenization problems in 2D by finite element method and collocation boundary element method. Theoretical results are confirmed by several numerical experiments.