An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation

作     者：Zhengru Zhang Zhonghua Qiao 

作者机构：Laboratory of Mathematics and Complex SystemsMinistry of EducationSchool of Mathematical SciencesBeijing Normal UniversityBeijing 100875China Institute for Computational Mathematics&Department of MathematicsHong Kong Baptist UniversityKowloon TongHong Kong 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2012年第11卷第4期

页      面：1261-1278页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：We would like to thank Prof.Houde Han of Tsinghua University and Prof.Qiang Du of Penn State University for their helpful discussions.Z.R.Zhang was supported by National NSF of China under Grant 10601007 Z.H.Qiao was supported by the FRG grants of the Hong Kong Baptist University under Grant No.FRG2/09-10/034 

主　　题：Adaptive time-stepping unconditionally energy stable Cahn-Hilliard equation mass conservation 

摘      要：This paper studies the numerical simulations for the Cahn-Hilliard equation which describes a phase separation *** numerical simulation of the Cahn-Hilliardmodel needs very long time to reach the steady state,and therefore large time-stepping methods become *** main objective of this work is to construct the unconditionally energy stable finite difference scheme so that the large time steps can be used in the numerical *** equation is discretized by the central difference scheme in space and fully implicit second-order scheme in *** proposed scheme is proved to be unconditionally energy stable and *** error estimate for the numerical solution is also obtained with second order in both space and *** using this energy stable scheme,an adaptive time-stepping strategy is proposed,which selects time steps adaptively based on the variation of the free energy against *** numerical experiments are presented to demonstrate the effectiveness of the adaptive time-stepping approach.