Second-Order Linear Stabilized Semi-Implicit Crank-Nicolson Scheme for the Cahn-Hilliard Model with Dynamic Boundary Conditions (Communications in Computational Physics, 2025)
We propose a kind of second-order stabilized Crank-Nicolson scheme whichcan be applied to three types of Cahn-Hilliard model with dynamic boundary conditions. We give the corresponding proof of stability and convergence theoreticallywhich 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’sfound that second-order scheme takes much less CPU time than the first-order schemeto reach the same final time.
Keywords: Cahn-Hilliard equation; dynamic boundary conditions; reaction rate; second-order Crank-Nicolson formula; energy stability; convergence analysis.