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A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
Liao, Hong-lin1; Tang, Tao2,3,4; Zhou, Tao5,6
2020-08-01
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
Volume414Pages:16
AbstractIn 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.
KeywordTime-fractional Allen-Cahn equation Alikhanov formula Adaptive time-stepping strategy Discrete maximum principle Sharp error estimate
DOI10.1016/j.jcp.2020.109473
Indexed BySCI
Language英语
Funding ProjectNUAA 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 Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000536532800011
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51473
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhou, Tao
Affiliation1.Nanjing Univ Aeronut & Astronaut, Dept Math, Nanjing 211106, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen, Guangdong, Peoples R China
3.Southern Univ Sci & Technol, Int Ctr Math, Shenzhen, Guangdong, Peoples R China
4.BNU HKBU United Int Coll, Div Sci & Technol, Zhuhai, Guangdong, Peoples R China
5.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing 100190, Peoples R China
6.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
Recommended Citation
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.
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