Two-Grid Finite Volume Element Methods for Solving Cahn-Hilliard Equation

This paper proposes a two-grid mixed finite volume element method (TGMFVE) that uses a ? time discrete scheme to solve the Cahn-Hilliard equation. This method is separated into two steps. In the first step, the solution of the Cahn-Hilliard equation can be obtained by using a mixed 0 scheme of the finite volume element method on a coarse grid using an iterative algorithm. The second step involves using the linearized mixed ? scheme finite volume element method to solve the equation on a fine grid. The stability analysis of the ? scheme of the two-grid mixed finite volume element method has been performed. The priori error estimation for L-2 norm and H-1 norm is also analyzed. The results of theoretical analysis are confirmed by numerical experiments. The results show that the theoretical results match the actual numerical results.