A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations

doi:10.1016/j.jcp.2020.109473

	A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
	Liao, Hong-lin 5; Tang, Tao 1,3,6; Zhou, Tao 2,4
刊名	JOURNAL OF COMPUTATIONAL PHYSICS
	2020-08-01
卷号	414 页码:16
关键词	Time-fractional Allen-Cahn equation Alikhanov formula Adaptive time-stepping strategy Discrete maximum principle Sharp error estimate
ISSN号	0021-9991
DOI	10.1016/j.jcp.2020.109473
英文摘要	In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of consistency error, we present sharp maximum-norm error estimates which reflect the temporal regularity. As our analysis is built on nonuniform time steps, we may resolve the intrinsic initial singularity by using the graded meshes. Moreover, we propose an adaptive time-stepping strategy for large time simulations. Numerical experiments are presented to show the effectiveness of the proposed scheme. This seems to be the first second-order maximum principle preserving scheme for the time-fractional Allen-Cahn equation. (c) 2020 Elsevier Inc. All rights reserved.
资助项目	NUAA Scientific Research Starting Fund of Introduced Talent[1008-56SYAH18037] ; NSF of China[11822111] ; NSF of China[11688101] ; NSF of China[91630203] ; NSF of China[11571351] ; NSF of China[11731006] ; Science Challenge Project[TZ2018001] ; NCMIS ; Youth Innovation Promotion Association, CAS
WOS研究方向	Computer Science ; Physics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000536532800011
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51472]
专题	中国科学院数学与系统科学研究院
通讯作者	Zhou, Tao
作者单位	1.BNU HKBU United Int Coll, Div Sci & Technol, Zhuhai, Guangdong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 3.Southern Univ Sci & Technol, Int Ctr Math, Shenzhen, Guangdong, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing 100190, Peoples R China 5.Nanjing Univ Aeronut & Astronaut, Dept Math, Nanjing 211106, Peoples R China 6.Southern Univ Sci & Technol, Dept Math, Shenzhen, Guangdong, Peoples R China
推荐引用方式 GB/T 7714	Liao, Hong-lin,Tang, Tao,Zhou, Tao. A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2020,414:16.
APA	Liao, Hong-lin,Tang, Tao,&Zhou, Tao.(2020).A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations.JOURNAL OF COMPUTATIONAL PHYSICS,414,16.
MLA	Liao, Hong-lin,et al."A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations".JOURNAL OF COMPUTATIONAL PHYSICS 414(2020):16.