Characteristic block-centred finite difference methods for nonlinear convection-dominated diffusion equation

摘要

In this article, two characteristic block-centred finite difference schemes are introduced and analysed to solve the nonlinear convection-dominated diffusion equation. One scheme is a linear difference approximation which shows that the discrete L-infinity(L-2) and L-2((H)1) errors are O(Delta t + h(2)), while the other is a two-grid scheme which demonstrates that the discrete L-infinity(L-2) and L-2(H-1) errors are O(Delta t + h(2) + H-3),, where h corresponds to a finer grid and H corresponds to a coarser grid. Error estimates with both schemes are established on a non-uniform rectangular grid. Finally, numerical experiments are presented to show that the convergence rates are in agreement with the theoretical analysis and validate the efficiency of the two-grid method.