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题名On energy dissipation theory and numerical stability for time-fractional phase-field equations
作者
发表日期2019
发表期刊SIAM Journal on Scientific Computing
ISSN/eISSN1064-8275
卷号41期号:6页码:A3757-A3778
摘要

For the time-fractional phase-field models, the corresponding energy dissipation law has not been well studied on both the continuous and the discrete levels. In this work, we address this open issue. More precisely, we prove for the first time that the time-fractional phase-field models indeed admit an energy dissipation law of an integral type. In the discrete level, we propose a class of finite difference schemes that can inherit the theoretical energy stability. Our discussion covers the time-fractional Allen-Cahn equation, the time-fractional Cahn-Hilliard equation, and the time-fractional molecular beam epitaxy models. Several numerical experiments are carried out to verify the theoretical predictions. In particular, it is observed numerically that for both the time-fractional Cahn-Hilliard equation and the time-fractional molecular beam epitaxy model, there exists a coarsening stage for which the energy dissipation rate satisfies a power law scaling with an asymptotic power - \alpha /3, where \alpha is the fractional parameter. 

关键词Allen-Cahn equation Cahn-Hilliard equation Energy dissipation law Maximum principle MBE model Time-fractional phase-field equations
DOI10.1137/18M1203560
URL查看来源
语种英语English
WOS研究方向Mathematics
WOS类目Mathematics, Applied
WOS记录号WOS:000549131500005
Scopus入藏号2-s2.0-85076698665
SciVal 热门主题T.15825
引用统计
被引频次:137[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符https://repository.uic.edu.cn/handle/39GCC9TT/1226
专题理工科技学院
通讯作者Tang, Tao
作者单位
1.Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guangdong, China
2.Shenzhen International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China
3.NCMIS \ and LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
4.School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
第一作者单位北师香港浸会大学
通讯作者单位北师香港浸会大学
推荐引用方式
GB/T 7714
Tang, Tao,Yu, Haijun,Zhou, Tao. On energy dissipation theory and numerical stability for time-fractional phase-field equations[J]. SIAM Journal on Scientific Computing, 2019, 41(6): A3757-A3778.
APA Tang, Tao, Yu, Haijun, & Zhou, Tao. (2019). On energy dissipation theory and numerical stability for time-fractional phase-field equations. SIAM Journal on Scientific Computing, 41(6), A3757-A3778.
MLA Tang, Tao,et al."On energy dissipation theory and numerical stability for time-fractional phase-field equations". SIAM Journal on Scientific Computing 41.6(2019): A3757-A3778.
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