In this paper we introduce and analyze a two-level Schwarz additive domain decomposition method used as a preconditioner of a GMRES algorithm for solving unsymmetric systems arising from the finite volume element or covolume methods for elliptic problems. The subproblems are solved by inexact solvers. We show that the method converges for both circumcentric and barycentric covolume methods. In the generous overlap case, the method is shown to be optimal, i.e., the conditioner number is uniformly bounded in coarse and fine mesh sizes.
Copyright 2003, Walter de Gruyter