Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection

doi:10.1007/s11425-020-1817-4

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	Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection
	Liao, Hong-Lin 1; Song, Xuehua 1; Tang, Tao 2,3,4; Zhou, Tao 5,6
	2021-02-11
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
页码	16
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
DOI	10.1007/s11425-020-1817-4
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[12071216] ; National Natural Science Foundation of China[11731006] ; National Natural Science Foundation of China[11822111] ; National Natural Science Foundation of China[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
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58189
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.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
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,2021:16.
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,16.
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):16.