A Decoupled, Linearly Implicit and Unconditionally Energy Stable Scheme for the Coupled Cahn-Hilliard Systems
Year: 2025
Author: Dan Zhao, Dongfang Li, Yanbin Tang, Jinming Wen
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 708–730
Abstract
We present a decoupled, linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard system. The time-discretization is done by leap-frog method with the scalar auxiliary variable (SAV) approach. It only needs to solve three linear equations at each time step, where each unknown variable can be solved independently. It is shown that the semi-discrete scheme has second-order accuracy in the temporal direction. Such convergence results are proved by a rigorous analysis of the boundedness of the numerical solution and the error estimates at different time-level. Numerical examples are presented to further confirm the validity of the methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2402-m2023-0079
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 708–730
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Coupled Cahn-Hilliard system Leap-frog method Scalar auxiliary variable Error estimate.