Superconvergence analysis of a two-grid method for nonlinear hyperbolic equations

Abstract

In this paper, the superconvergence analysis of a second-order fully discrete scheme with two-grid method (TGM) is studied for the two-dimensional nonlinear hyperbolic equations by the bilinear finite element. The existence and uniqueness of the solution for the scheme are proved rigorously. By use of the combination technique of the interpolation and Ritz projection, the superclose results in H1-norm are obtained, and the global superconvergence is derived through the interpolated postprocessing approach. Finally, some numerical results are provided to verify the theoretical predictions and show the efficiency of the proposed TGM.