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 - <p style="text-align: justify;">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.</p>