@Article{CiCP-38-1210,
author = {Zhu , XiaohanGong , Yuezheng and Wang , Yushun},
title = {A Class of Second-Order Energy-Stable Schemes for the Cahn-Hilliard Equation and Their Linear Iteration Algorithm},
journal = {Communications in Computational Physics},
year = {2025},
volume = {38},
number = {4},
pages = {1210--1236},
abstract = {<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>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2024-0016},
url = {http://global-sci.org/intro/article_detail/cicp/24357.html}
}