High Order Compact Block-Centered Finite Difference Schemes for Elliptic and Parabolic Problems

Based on the combination of block-centered and compact difference methods, fourth order compact block-centered finite difference schemes for the numerical solutions of one-dimensional and two-dimensional elliptic and parabolic problems with variable coefficients are derived and analyzed. Stability and optimal fourth-order error estimates are proved for both the solution and flux. Numerical experiments for model problems are presented to confirm the theoretical results and superior performance of the proposed schemes.