COMBINATIONS OF THE RITZ-GALERKIN AND FINITE DIFFERENCE METHODS

This paper presents six combinations of the Ritz-Galerkin method and the finite difference method for solving elliptic boundary value problems. Not only optimal convergence rates of solutions but also superconvergence rates of solution derivatives can be achieved. The non-conforming combination and other five new combinations are given in algorithms, error analysis, convergence rates, outlines of proofs, numerical experiments and their comparisons