KMS Of Academy of mathematics and systems sciences, CAS
| Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection | |
| Liao, Hong-Lin1; Song, Xuehua1; Tang, Tao2,3,4; Zhou, Tao5,6 | |
| 2021-02-11 | |
| Source Publication | SCIENCE CHINA-MATHEMATICS
 |
| ISSN | 1674-7283 |
| Pages | 16 |
| Abstract | 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. |
| Keyword | molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis |
| DOI | 10.1007/s11425-020-1817-4 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000616868300001 |
| Publisher | SCIENCE PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58189 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Tang, Tao |
| Affiliation | 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 |
| Recommended Citation 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. |
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