Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy

Chen，Wenbin1; Li，Weijia2; Wang，Cheng3; Wang，Shufen2; Wang，Xiaoming4

2020-09-01

10.1007/s40687-020-00212-9

Research in the Mathematical Sciences   影响因子和分区

2522-0144

2197-9847

We discuss how to combine exponential time differencing technique with multi-step method to develop higher order in time linear numerical scheme that are energy stable for certain gradient flows with the aid of a generalized viscous damping term. As an example, a stabilized third order in time accurate linear exponential time differencing (ETD) scheme for the epitaxial thin film growth model without slope selection is proposed and analyzed. An artificial stabilizing term Aτ3∂Δ3u∂t is added to ensure energy stability, with ETD-based multi-step approximations and Fourier pseudo-spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long-time energy stability and an ℓ(0 , T; ℓ) error analysis are provided, based on the energy method. In addition, a few numerical experiments are presented to demonstrate the energy decay and convergence rate.

Convergence analysis Epitaxial thin film growth Exponential time differencing Gradient flow Long-time energy stability Third-order scheme

SCI

英语

通讯

NSFC[11671098][91630309] ; 111 Project[B08018] ; NSF[DMS-1418689] ; Guangdong Provincial Key Laboratory for Computational Science and Material Design[2019B030301001] ; [NSFC11871159]

Mathematics

Mathematics

WOS:000544010300001

SPRINGER INTERNATIONAL PUBLISHING AG

2-s2.0-85087132550

Scopus

1.Shanghai Key Laboratory of Mathematics for Nonlinear Sciences,School of Mathematical Sciences,Fudan University,Shanghai,200433,China
2.School of Mathematical Sciences,Fudan University,Shanghai,200433,China
3.Mathematics Department,University of Massachusetts,North Dartmouth,02747,United States
4.SUSTech International Center for Mathematics and Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China

Chen，Wenbin,Li，Weijia,Wang，Cheng,et al. Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy[J]. Research in the Mathematical Sciences,2020,7(3).

Chen，Wenbin,Li，Weijia,Wang，Cheng,Wang，Shufen,&Wang，Xiaoming.(2020).Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy.Research in the Mathematical Sciences,7(3).

Chen，Wenbin,et al."Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy".Research in the Mathematical Sciences 7.3(2020).