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Volume 35, Issue 6
A Second-Order Convex Splitting Scheme for a Cahn-Hilliard Equation with Variable Interfacial Parameters

Xiao Li, Zhonghua Qiao & Hui Zhang

DOI: 10.4208/jcm.1611-m2016-0517

J. Comp. Math., 35 (2017), pp. 693-710.

Published online: 2017-12

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M06, 65M12, 65Z05.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lixiao1228@163.com (Xiao Li)

zqiao@polyu.edu.hk (Zhonghua Qiao)

hzhang@bnu.edu.cn (Hui Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-35-693, author = {Li , XiaoQiao , Zhonghua and Zhang , Hui}, title = {A Second-Order Convex Splitting Scheme for a Cahn-Hilliard Equation with Variable Interfacial Parameters}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1611-m2016-0517}, url = {http://global-sci.org/intro/article_detail/jcm/10490.html} }
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 -

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.

Li , XiaoQiao , Zhonghua and Zhang , Hui. (2017). A Second-Order Convex Splitting Scheme for a Cahn-Hilliard Equation with Variable Interfacial Parameters. Journal of Computational Mathematics. 35 (6). 693-710. doi:10.4208/jcm.1611-m2016-0517
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