A Class of Second-Order Energy-Stable Schemes for the Cahn-Hilliard Equation and Their Linear Iteration Algorithm (Communications in Computational Physics, 2025)
In this paper, we study a class of second-order accurate and energy-stablenumerical schemes for the Cahn-Hilliard model. These schemes are constructed bycombining the Crank-Nicolson approximation with three stabilization terms in timeand employing the Fourier pseudo-spectral method in space. This class of schemesincludes the second-order schemes presented in previous works while providing newschemes by introducing stabilization terms. To solve these schemes with strong nonlinearity efficiently, we propose a linear iteration algorithm and prove that the algorithmsatisfies a contraction mapping property in the discrete $l^4$ norm. Furthermore, weestablish a comprehensive theoretical analysis, including unique solvability, mass conservation, energy stability, and convergence based on a uniform-in-time $l^∞$ bound ofthe numerical solution for the proposed second-order scheme. Some numerical simulation results with many different sets of stabilization parameters are presented toconclude the paper.