Local Refinement Techniques for Elliptic Problems on Cell-centered Grids; II. Optimal Order Two-grid Iterative Methods.

Two preconditioning techniques for solving difference equations arising infinite difference approximation of elliptic problems on cell-centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher-order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG-LS in the nonsymmetric case) are presented. [ABSTRACT FROM AUTHOR]