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A Second-Order Convex Splitting Scheme for a Cahn-Hilliard Equation with Variable Interfacial Parameters

A Second-Order Convex Splitting Scheme for a Cahn-Hilliard Equation with Variable Interfacial Parameters
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Year:    2017

Author:    Xiao Li, Zhonghua Qiao, Hui Zhang

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 6 : pp. 693–710

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1611-m2016-0517

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 6 : pp. 693–710

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Cahn-Hilliard equation Second-order accuracy Convex splitting Energy stability.

Author Details

Xiao Li

Zhonghua Qiao

Hui Zhang

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