TY - JOUR
T1 - A Class of Second-Order Energy-Stable Schemes for the Cahn-Hilliard Equation and Their Linear Iteration Algorithm
AU - Zhu , Xiaohan
AU - Gong , Yuezheng
AU - Wang , Yushun
JO - Communications in Computational Physics
VL - 4
SP - 1210
EP - 1236
PY - 2025
DA - 2025/09
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0016
UR - https://global-sci.org/intro/article_detail/cicp/24357.html
KW - Cahn-Hilliard equation, second-order energy-stable scheme, Fourier pseudo-spectral method, energy stability, linear iteration.
AB - <p style="text-align: justify;">In this paper, we study a class of second-order accurate and energy-stable
numerical schemes for the Cahn-Hilliard model. These schemes are constructed by
combining the Crank-Nicolson approximation with three stabilization terms in time
and employing the Fourier pseudo-spectral method in space. This class of schemes
includes the second-order schemes presented in previous works while providing new
schemes by introducing stabilization terms. To solve these schemes with strong nonlinearity efficiently, we propose a linear iteration algorithm and prove that the algorithm
satisfies a contraction mapping property in the discrete $l^4$ norm. Furthermore, we
establish a comprehensive theoretical analysis, including unique solvability, mass conservation, energy stability, and convergence based on a uniform-in-time $l^∞$ bound of
the numerical solution for the proposed second-order scheme. Some numerical simulation results with many different sets of stabilization parameters are presented to
conclude the paper.</p>