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 in finite 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.