Abstract: A time two-mesh (TT-M) finite element (FE) method is proposed for solving the Cahn-Hilliard equation in a nonlinear numerical scheme. The method is carried out in two steps. A nonlinear Cahn-Hilliard system is solved on time coarse mesh at the first step, where the finite element method is used for spatial discretisation, and the Crank-Nicolson scheme is used for time discretisation. The second step is that a linear problem is solved on time fine mesh. Finally, the stability analysis and error estimates of the proposed method is given. Numerical examples are given to confirm the theoretical analysis. The results show that the method of this paper can save computation time compared with the traditional Galerkin finite element method. The validity and feasibility of the proposed method are illustrated.

Key words: Cahn-Hilliard equation, TT-M FE method, stability, error estimate, CPU time