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http://hdl.handle.net/10397/60936
| 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 (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), 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: http://dx.doi.org/10.1007/s11425-016-5137-2 ttps://doi.org/ |
| Appears in Collections: | Journal/Magazine Article |
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| Qiao_Unconditionally_Energy_Stable.pdf | Pre-Published version | 1.26 MB | Adobe PDF | View/Open |
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