ON ENERGY DISSIPATION THEORY AND NUMERICAL STABILITY FOR TIME-FRACTIONAL PHASE-FIELD EQUATIONS

doi:10.1137/18M1203560

	ON ENERGY DISSIPATION THEORY AND NUMERICAL STABILITY FOR TIME-FRACTIONAL PHASE-FIELD EQUATIONS
	Tang, Tao 1,3; Yu, Haijun 2,4; Zhou, Tao 2
刊名	SIAM JOURNAL ON SCIENTIFIC COMPUTING
	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
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000549131500005
内容类型	期刊论文
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.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS & LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 3.BNU HKBU United Int Coll, Div Sci & Technol, Zhuhai, Guangdong, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, 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.