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Title: An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation
Authors: Li, X
Qiao, Z 
Zhang, H
Keywords: Adaptive time stepping
Cahn-Hilliard equation
Convex splitting
Energy stability
Stochastic term
Issue Date: 2016
Publisher: Science in China Press
Source: Science China. Mathematics, 2016, v. 59, no. 9, p. 1815-1834 How to cite?
Journal: Science China. Mathematics 
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.
ISSN: 1674-7283
DOI: 10.1007/s11425-016-5137-2
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