南方科技大学知识苑(SUSTech KC): On energy dissipation theory and numerical stability for time-fractional phase-field equations

题名	On energy dissipation theory and numerical stability for time-fractional phase-field equations
作者	Tang，Tao1,2 ; Yu，Haijun 3,4; Zhou，Tao 3
发表日期	2019
DOI	10.1137/18M1203560
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING 影响因子和分区
ISSN	1064-8275
EISSN	1095-7197
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
相关链接	[Scopus记录]
收录类别	EI ; SCI
语种	英语
重要成果	ESI高被引
学校署名	其他
资助项目	National Natural Science Foundation of China[11571351] ; National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[11731006] ; National Natural Science Foundation of China[11771439] ; National Basic Research Program of China (973 Program)[2015CB856003] ; National Natural Science Foundation of China[91530322] ; National Natural Science Foundation of China[91630203] ; National Natural Science Foundation of China[91630312] ; National Basic Research Program of China (973 Program)[TZ2018001]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000549131500005
出版者	Society for Industrial and Applied Mathematics Publications
EI入藏号	20195207903278
EI主题词	Coarsening ; Finite difference method ; Maximum principle ; Molecular beam epitaxy ; Molecular beams ; Two phase flow
EI分类号	Energy Losses (industrial and residential):525.4 ; Fluid Flow, General:631.1 ; Numerical Methods:921.6 ; Atomic and Molecular Physics:931.3 ; Materials Science:951
ESI学科分类	MATHEMATICS
Scopus记录号	2-s2.0-85076698665
来源库	Scopus
引用统计	被引频次[WOS]：115
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/65401
专题	南方科技大学深圳国际数学中心（杰曼诺夫数学中心）（筹）
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	南方科技大学
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.