Please use this identifier to cite or link to this item:
PIRA download icon_1.1View/Download Full Text
Title: An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation
Authors: Li, X
Qiao, Z 
Zhang, H
Issue Date: Sep-2016
Source: Science China. Mathematics, Sept. 2016, v. 59, no. 9, p. 1815-1834
Abstract: In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.
Keywords: Adaptive time stepping
Cahn-Hilliard equation
Convex splitting
Energy stability
Stochastic term
Publisher: Springer
Journal: Science China. Mathematics 
ISSN: 1674-7283
DOI: 10.1007/s11425-016-5137-2
Rights: © Science China Press and Springer-Verlag Berlin Heidelberg 2016
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:
Appears in Collections:Journal/Magazine Article

Files in This Item:
File Description SizeFormat 
Qiao_Unconditionally_Energy_Stable.pdfPre-Published version1.26 MBAdobe PDFView/Open
Open Access Information
Status open access
File Version Final Accepted Manuscript
View full-text via PolyU eLinks SFX Query
Show full item record

Page views

Last Week
Last month
Citations as of Sep 24, 2023


Citations as of Sep 24, 2023


Last Week
Last month
Citations as of Sep 28, 2023


Last Week
Last month
Citations as of Sep 28, 2023

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.