Two-level methods for the Cahn-Hilliard equation

We propose the fully discrete traditional finite element and mixed finite element two-level schemes for solving the Cahn-Hilliard equation in the paper. We give the stability and convergence of the traditional finite element and mixed finite element two-level methods. The analysis shows that the two-level methods can get the same convergence as the one-level methods provided that we choose proper coarse and fine mesh sizes. However, the two-level methods can save much computational time compared with the one-level methods. Finally, some numerical experiments are provided to confirm the theoretical analysis. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.