On domain decomposition algorithms for covolume methods for elliptic problems

In this paper, some new two-level additive Schwarz domain decomposition methods are constructed and used as preconditioners for GMRES for the nonsymmetric systems arising from the covolume methods for elliptic problems. Without any restriction on the coarse mesh size, the convergence of the preconditioned GMRES is obtained for both circumcentric and barycentric covolume methods with inexact solvers for subproblems. The rates of convergence are shown to be independent of the number of subregions and these methods are optimal for generous overlap.