Preconditioning for heterogeneous problems

Abstract

The main focus of this paper is to suggest a domain decomposition method for mixed finite element approximations of elliptic problems with anisotropic coefficients in domains. The theorems on traces of functions from Sobolev spaces play an important role in studying boundary value problems of partial differential equations. These theorems are commonly used for a priori estimates of the stability with respect to boundary conditions, and also play very important role in constructing and studying effective domain decomposition methods. The trace theorem for anisotropic rectangles with anisotropic grids is the main tool in this paper to construct domain decomposition preconditioners.