发表状态 | 已发表Published |
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
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ISSN/eISSN | 1064-8275 |
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 |
DOI | 10.1137/18M1203560 |
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 | |
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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Tang-2019-On energy (1073KB) | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | 浏览 下载 |
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