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A symmetric and a nonsymmetric variant of the additive Schwarz preconditionerare proposed for the solution of a nonsymmetric system of algebraic equationsarising from a general finite volume element discretization of symmetricelliptic problems with large jumps in the entries of the coefficient matricesacross subdomains. It is shown in the analysis, that the convergence of thepreconditioned GMRES iteration with the proposed preconditioners, dependspolylogarithmically on the mesh parameters, in other words, the convergence isonly weakly dependent on the mesh parameters, and it is robust with respect tothe jumps in the coefficients.

Additive Schwarz preconditioner for the general finite volume element discretization of symmetric elliptic problems