Additive Average Schwarz Method for a Crouzeix-Raviart Finite Volume Element Discretization of Elliptic Problems
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 inside subdomains and across subdomain boundaries. The proposed methods depends linearly or quadratically on the mesh parameters H∕h, i.e., depending on the distribution of the coefficient in the model problem, the parameters describing the convergence of the GMRES method used to solve the preconditioned system depends linearly or quadratically on the mesh parameters. Also, under certain restrictions on the distribution of the coefficient, the convergence of the GMRES method is independent of jumps in the coefficient.
This work was partially supported by Polish Scientific Grant 2011/01/ B/ST1/01179 (Leszek Marcinkowski).
- 6.S.C Eisenstat, H.C Elman, M.H Schultz, Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20(2), 345–357 (1983)Google Scholar
- 11.Y. Saad, M.H Schultz, Gmres: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856–869 (1986)Google Scholar
- 15.A. Toselli, O.B Widlund, Domain Decomposition Methods: Algorithms and Theory, vol. 34 (Springer, New York, 2005)Google Scholar