Two-grid P_0~2-P_1 mixed finite element methods combined with Crank-Nicolson scheme for a class of nonlinear parabolic equations

摘要

In this paper, we discuss a priori error estimates of two-grid mixed finite element methods for a class of nonlinear parabolic equations. The gradient for the method belongs to the square integrable space instead of the classical H(div; Omega) space. P-0(2)-P-1 mixed finite elements and Crank-Nicolson method are used for the spatial and temporal discretization. First, we derive the optimal a priori error estimates for all variables. Second, we present a two-grid scheme and analyze its convergence. It is shown that when the two mesh sizes satisfy h = H-2, the two-grid method achieves the same convergence property as the P-0(2)-P-1 mixed finite element method. Finally, we give a numerical example to verify the theoretical results. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.