A new symmetric mixed element method for semi-linear parabolic problem based on two-grid discretization

Abstract

Based on two-grid discretization, a new numerical method is constructed for semilinear parabolic problem. In this method, a new symmetric positive definite numerical scheme is provided, and then the optimal a priori error estimates in L2 and Lp-norm are given. In order to improve the efficiency of computation, the two-grid method is considered. The corresponding convergence analysis is studied, and the optimal error estimate is derived under the relation h=O(H2). Some numerical experiments are presented to confirm our theoretical analysis.