A two-grid block-centered finite difference method for nonlinear non-Fickian flow model

In this paper, a two-grid block-centered finite difference scheme is introduced and analyzed to solve the nonlinear parabolic integro-differential equation arising in modeling non-Fickian flow in porous media. This method is considered where the nonlinear problem is solved only on a coarse grid of size H and a linear problem is solved on a fine grid of size h. Error estimates are established on non-uniform rectangular grid which show that the discrete L∞(L2) and L2(H1) errors are O(▵t+h2+H3)O(▵t+h2+H3). Finally, some numerical experiments are presented to show the efficiency of the two-grid method and verify that the convergence rates are in agreement with the theoretical analysis.