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A Decoupled, Linearly Implicit and Unconditionally Energy Stable Scheme for the Coupled Cahn-Hilliard Systems

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.

Author Details

Dan Zhao

Dongfang Li

Yanbin Tang

Jinming Wen