Edge based Schwarz methods for the Crouzeix-Raviart finite volume element discretization of elliptic problems

In this paper, we present two variants of the Additive Schwarz Method for a Crouzeix-Raviart finite volume element (CRFVE) discretization of second order elliptic problems with discontinuous coefficients where the discontinuities are only across subdomain boundaries. One preconditioner is symmetric while the other is nonsymmetric. The proposed methods are almost optimal, in the sense that the residual error estimates for the GMRES iteration in the both cases depend only polylogarithmically on the mesh parameters.