The main focus of this paper is to suggest a domain decomposition method for finite element approximations of elliptic problems with anisotropic coecients in domains consisting of anisotropic shape rectangles. The theorems on traces of functions from Sobolev spaces pla y an important role in studying boundary value problems of partial difierential equations. These theorems are commonly used for a priori estimates of the stability with resp ect to boundary conditions, and also play very important role in constructing and investigating 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.
Key words: Domain Decomposition Method, Anisotropic Problem, Trace Theorem