Two-grid methods of expanded mixed finite-element solutions for nonlinear parabolic problems

Abstract

In this paper, we propose two efficient two-grid algorithms for the nonlinear parabolic equations by using expanded mixed finite element methods. To linearize the finite element equations, two-grid algorithms based on some Newton iteration approach and correction method are applied. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h1/3) (or H=O(h1/4)). Experiments are presented to show the efficiency and effectiveness of the two-grid methods.