Some developments of homogenization theory and Rothe's method

This thesis is devoted to homogenization theory and some generalizations of Rothe's method to non-cylindrical domains. It consists of two introductory chapters and four papers. Chapters 1 and 2 serve as a self-contained overview to the theory of homogenization. In the introduction we present the idea behind homogenization theory and in the second chapter some further results in homogenization theory are presented and some of the homogenization results from chapter 1 are proved. Paper A deals with a numerical study of stochastic homogenization and paper B deals with some generalizations of Rothe's method to non-cylindrical domains. Paper C is devoted to numerical analysis of the convergence in homogenization of composites and finally the degeneracy in stochastic homogenization is considered in the paper D.Godkänd; 2005; 20070103 (haneit