Second-Order Linear Stabilized Semi-Implicit Crank-Nicolson Scheme for the Cahn-Hilliard Model with Dynamic Boundary Conditions

Abstract

We propose a kind of second-order stabilized Crank-Nicolson scheme which can be applied to three types of Cahn-Hilliard model with dynamic boundary conditions. We give the corresponding proof of stability and convergence theoretically which takes the reaction rate dependent dynamic boundary conditions as an example. We verify the effectiveness and universality of our proposed scheme by conducting some typical numerical simulations and comparing with the literature works. It’s found that second-order scheme takes much less CPU time than the first-order scheme to reach the same final time.