A SECOND-ORDER CONVEX SPLITTING SCHEME FOR A CAHN-HILLIARD EQUATION WITH VARIABLE INTERFACIAL PARAMETERS

• 来源期刊: 计算数学（英文版）
• 关键词: Cahn-Hilliard equation Second-order accuracy Convex splitting Energy stability
• 年，卷（期）: 2017,（6）
• 页码范围: 693-710
• 页数: 18页
• 语种: 英文
• DOI: 10.4208/jcm.1611-m2016-0517

摘要

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.