ON ENERGY DISSIPATION THEORY AND NUMERICAL STABILITY FOR TIME-FRACTIONAL PHASE-FIELD EQUATIONS
文献类型：期刊论文
| 作者 | Tang, Tao1,3; Yu, Haijun2,4; Zhou, Tao4 |
| 刊名 | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| 出版日期 | 2019 |
| 卷号 | 41期号:6页码:A3757-A3778 |
| 关键词 | time-fractional phase-field equations Allen-Cahn equation Cahn-Hilliard equation MBE model energy dissipation law maximum principle |
| ISSN号 | 1064-8275 |
| DOI | 10.1137/18M1203560 |
| 英文摘要 | 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. |
| 资助项目 | NNSF of China[11688101] ; NNSF of China[11771439] ; NNSF of China[91530322] ; NNSF of China[91630312] ; NNSF of China[91630203] ; NNSF of China[11571351] ; NNSF of China[11731006] ; China National Program on Key Basic Research Project[2015CB856003] ; Science Challenge Project[TZ2018001] ; NCMIS ; Youth Innovation Promotion Association (CAS) |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000549131500005 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51825]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Tang, Tao |
| 作者单位 | 1.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Shenzhen 518055, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China 3.BNU HKBU United Int Coll, Div Sci & Technol, Zhuhai, Guangdong, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS & LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。