An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

Xiao Li, Zhonghua Qiao, Hui Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1815-1834
Number of pages20
JournalScience China Mathematics
Volume59
Issue number9
DOIs
Publication statusPublished - 1 Sep 2016

Keywords

  • adaptive time stepping
  • Cahn-Hilliard equation
  • convex splitting
  • energy stability
  • stochastic term

ASJC Scopus subject areas

  • Mathematics(all)

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