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In this paper, we present two variants of the Additive Schwarz Method for aCrouzeix-Raviart finite volume element (CRFVE) discretization of second orderelliptic problems with discontinuous coefficients where the discontinuities areonly across subdomain boundaries. One preconditioner is symmetric while theother is nonsymmetric. The proposed methods are almost optimal, in the sensethat the residual error estimates for the GMRES iteration in the both casesdepend only polylogarithmically on the mesh parameters.

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