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.