ON ENERGY STABLE, MAXIMUM-PRINCIPLE PRESERVING, SECOND-ORDER BDF SCHEME WITH VARIABLE STEPS FOR THE ALLEN-CAHN EQUATION

doi:10.1137/19M1289157

	ON ENERGY STABLE, MAXIMUM-PRINCIPLE PRESERVING, SECOND-ORDER BDF SCHEME WITH VARIABLE STEPS FOR THE ALLEN-CAHN EQUATION
	Liao, Hong-lin 1; Tang, Tao 2,3; Zhou, Tao 4,5
刊名	SIAM JOURNAL ON NUMERICAL ANALYSIS
	2020
卷号	58 期号:4 页码:2294-2314
关键词	Allen-Cahn equation nonuniform BDF2 scheme energy stability discrete maximum principle convergence analysis
ISSN号	0036-1429
DOI	10.1137/19M1289157
英文摘要	In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is energy stable under the time-step ratio restriction r(k) := tau(k)/tau(k)(-1) < (3 + root 17)/2 approximate to 3.561. Moreover, by developing a novel kernel recombination and complementary technique, we show, for the first time, the discrete maximum bound principle of the BDF2 scheme under the time-step ratio restriction r(k) < 1 + root 2 approximate to 2.414 and a practical time-step constraint. The second-order rate of convergence in the maximum norm is also presented. Numerical experiments are provided to support the theoretical findings.
资助项目	NUAA Scientific Research Starting Fund of Introduced Talent grant[1008-56SYAH18037] ; National Natural Science Foundation of China[11731006] ; National Natural Science Foundation of China[11822111] ; National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[11571351] ; 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:000568220000012
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52169]
专题	中国科学院数学与系统科学研究院
通讯作者	Liao, Hong-lin
作者单位	1.Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211106, Peoples R China 2.SUSTech Int Ctr Math, Shenzhen, 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, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing 100190, Peoples R China 5.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liao, Hong-lin,Tang, Tao,Zhou, Tao. ON ENERGY STABLE, MAXIMUM-PRINCIPLE PRESERVING, SECOND-ORDER BDF SCHEME WITH VARIABLE STEPS FOR THE ALLEN-CAHN EQUATION[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2020,58(4):2294-2314.
APA	Liao, Hong-lin,Tang, Tao,&Zhou, Tao.(2020).ON ENERGY STABLE, MAXIMUM-PRINCIPLE PRESERVING, SECOND-ORDER BDF SCHEME WITH VARIABLE STEPS FOR THE ALLEN-CAHN EQUATION.SIAM JOURNAL ON NUMERICAL ANALYSIS,58(4),2294-2314.
MLA	Liao, Hong-lin,et al."ON ENERGY STABLE, MAXIMUM-PRINCIPLE PRESERVING, SECOND-ORDER BDF SCHEME WITH VARIABLE STEPS FOR THE ALLEN-CAHN EQUATION".SIAM JOURNAL ON NUMERICAL ANALYSIS 58.4(2020):2294-2314.