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Volume 43, Issue 3
A Decoupled, Linearly Implicit and Unconditionally Energy Stable Scheme for the Coupled Cahn-Hilliard Systems

Dan Zhao, Dongfang Li, Yanbin Tang & Jinming Wen

DOI: 10.4208/jcm.2402-m2023-0079

J. Comp. Math., 43 (2025), pp. 708-730.

Published online: 2024-11

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  • 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.

  • Keywords

Coupled Cahn-Hilliard system, Leap-frog method, Scalar auxiliary variable, Error estimate.

  • AMS Subject Headings

65M12, 65M22, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-708, author = {Zhao , DanLi , DongfangTang , Yanbin and Wen , Jinming}, title = {A Decoupled, Linearly Implicit and Unconditionally Energy Stable Scheme for the Coupled Cahn-Hilliard Systems}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {43}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2402-m2023-0079}, url = {http://global-sci.org/intro/article_detail/jcm/23556.html} }
TY - JOUR T1 - A Decoupled, Linearly Implicit and Unconditionally Energy Stable Scheme for the Coupled Cahn-Hilliard Systems AU - Zhao , Dan AU - Li , Dongfang AU - Tang , Yanbin AU - Wen , Jinming JO - Journal of Computational Mathematics VL - 3 SP - 708 EP - 730 PY - 2024 DA - 2024/11 SN - 43 DO - http://doi.org/10.4208/jcm.2402-m2023-0079 UR - https://global-sci.org/intro/article_detail/jcm/23556.html KW - Coupled Cahn-Hilliard system, Leap-frog method, Scalar auxiliary variable, Error estimate. AB -

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.

Zhao , DanLi , DongfangTang , Yanbin and Wen , Jinming. (2024). A Decoupled, Linearly Implicit and Unconditionally Energy Stable Scheme for the Coupled Cahn-Hilliard Systems. Journal of Computational Mathematics. 43 (3). 708-730. doi:10.4208/jcm.2402-m2023-0079
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