Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection  被引量:4

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作  者:Hong-Lin Liao Xuehua Song Tao Tang Tao Zhou 

机构地区:[1]Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211101,China [2]Department of Mathematics and International Center for Mathematics,Southern University of Science and Technology,Shenzhen 518055,China [3]Division of Science and Technology,BNU-HKBU United International College,Zhuhai 519087,China [4]NCMIS&LSEC,Institute of Computational Mathematics and Scientific Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出  处:《Science China Mathematics》2021年第5期887-902,共16页中国科学:数学(英文版)

基  金:supported by National Natural Science Foundation of China(Grant No.12071216);supported by National Natural Science Foundation of China(Grant No.11731006);the NNW2018-ZT4A06 project;supported by National Natural Science Foundation of China(Grant Nos.11822111,11688101 and 11731006);the Science Challenge Project(Grant No.TZ2018001)。

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):=τ_(k)/τ_(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 

分 类 号:O241.84[理学—计算数学]

 

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