Multiscale Analysis For Layered Composite Materials And Anisotropic Finite Element Method

The main part of this paper deals with computation of the heat transfer problems of the layered composite materials. Firstly,we discuss non-homogeneous boundary Dirichlet problem of layered composite materials by using of asymptotic expansion and homogenization and obtain the homogenized equation and the asymptotic expansion. We provide a detailed convergence analysis of this problem. Secondly,a kind of homogenized equation of homogenous boundary Dirichlet problem can be analysed by mixed finite element method. We give an numerical scheme. This element spaces have the characteristic of anisotropic, that is to say,the domain subdivision need not satisfy the regular condition. The anisotropic interpolation theory can be used to give error estimation.