南方科技大学知识苑(SUSTech KC): Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection

题名	Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection
作者	Liao, Hong-Lin 1; Song, Xuehua 1; Tang, Tao2,3,4 ; Zhou, Tao 5,6
通讯作者	Tang, Tao
发表日期	2021-02-01
DOI	10.1007/s11425-020-1817-4
发表期刊	Science China-Mathematics 影响因子和分区
ISSN	1674-7283
EISSN	1869-1862
摘要	In this work, we are concerned with the stability and convergence analysis of the second-order backward difference formula (BDF2) with variable steps for the molecular beam epitaxial model without slope selection. We first show that the variable-step BDF2 scheme is convex and uniquely solvable under a weak time-step constraint. Then we show that it preserves an energy dissipation law if the adjacent time-step ratios satisfy r(k):= tau(k)/tau(k-1) < 3.561. Moreover, with a novel discrete orthogonal convolution kernels argument and some new estimates on the corresponding positive definite quadratic forms, the L-2 norm stability and rigorous error estimates are established, under the same step-ratio constraint that ensures the energy stability, i.e., 0 < r(k) < 3.561. This is known to be the best result in the literature. We finally adopt an adaptive time-stepping strategy to accelerate the computations of the steady state solution and confirm our theoretical findings by numerical examples.
关键词	molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis
相关链接	[来源记录]
收录类别	SCI
语种	英语
重要成果	ESI高被引
学校署名	通讯
资助项目	National Natural Science Foundation of China[12071216,11731006,11822111,11688101] ; Science Challenge Project[TZ2018001] ; [NNW2018-ZT4A06]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000616868300001
出版者	SCIENCE PRESS
来源库	Web of Science
引用统计	被引频次[WOS]：41
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/221267
专题	理学院_数学系深圳国际数学中心（杰曼诺夫数学中心）（筹）
作者单位	1.Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211101, Peoples R China 2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China 3.Southern Univ Sci & Technol, Int Ctr Math, Shenzhen 518055, Peoples R China 4.BNU HKBU United Int Coll, Div Sci & Technol, Zhuhai 519087, 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
通讯作者单位	数学系; 南方科技大学
推荐引用方式 GB/T 7714	Liao, Hong-Lin,Song, Xuehua,Tang, Tao,et al. Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection[J]. Science China-Mathematics,2021.
APA	Liao, Hong-Lin,Song, Xuehua,Tang, Tao,&Zhou, Tao.(2021).Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection.Science China-Mathematics.
MLA	Liao, Hong-Lin,et al."Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection".Science China-Mathematics (2021).