TY - JOUR
T1 - A Second-Order Convex Splitting Scheme for a Cahn-Hilliard Equation with Variable Interfacial Parameters
AU - Li , Xiao
AU - Qiao , Zhonghua
AU - Zhang , Hui
JO - Journal of Computational Mathematics
VL - 6
SP - 693
EP - 710
PY - 2017
DA - 2017/12
SN - 35
DO - http://doi.org/10.4208/jcm.1611-m2016-0517
UR - https://global-sci.org/intro/article_detail/jcm/10490.html
KW - Cahn-Hilliard equation, Second-order accuracy, Convex splitting, Energy stability.
AB - <p style="text-align: justify;">In this paper, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation with a variable interfacial parameter, is solved numerically by using a convex splitting scheme which is second-order in time for the non-stochastic part in combination with the Crank-Nicolson and the Adams-Bashforth methods. For the non-stochastic case, the unconditional energy stability is obtained in the sense that a modified energy is non-increasing. The scheme in the stochastic version is then obtained by adding the discretized stochastic term. Numerical experiments are carried out to verify the second-order convergence rate for the non-stochastic case, and to show the long-time stochastic evolutions using larger time steps.</p>