Conservative nonlinear difference scheme for the Cahn-Hilliard equation

Numerical solutions for the Cahn-Hilliard equation is considered using the Crank-Nicolson type finite difference method. Existence of the solution for the difference scheme has been shown by Brouwer fixed-point theorem. Stability, convergence and error analysis of the scheme are shown. We also show that the scheme preserves the discrete mass, even though the linearized scheme in [1] is conditionally stable and does not preserve the mass.