Additive average Schwarz method for a Crouzeix-Raviart Finite Volume Element Discretization of Elliptic Problems with Heterogeneous Coefficients
This work addresses the need for scalable solvers for finite volume element discretizations of elliptic problems with heterogeneous coefficients, a challenge in computational science and engineering.
The paper proposes an additive Schwarz method for Crouzeix-Raviart Finite Volume Element discretization of elliptic problems with discontinuous coefficients, achieving GMRES convergence rates that depend linearly or quadratically on mesh parameters H/h, and in some cases are independent of coefficient jumps.
In this paper we introduce an additive Schwarz method for a Crouzeix-Raviart Finite Volume Element (CRFVE) discretization of a second order elliptic problem with discontinuous coefficients, where the discontinuities are both inside the subdomains and across and along the subdomain boundaries. We show that, depending on the distribution of the coefficient in the model problem, the parameters describing the GMRES convergence rate of the proposed method depend linearly or quadratically on the mesh parameters $H/h$. Also, under certain restrictions on the distribution of the coefficient, the convergence of the GMRES method is independent of jumps in the coefficient.