Volume 54, Number 3, May-June 2020
|Page(s)||727 - 750|
|Published online||01 April 2020|
A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection
Shanghai Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, 200433 Shanghai, P.R. China
2 School of Mathematical Sciences, Fudan University, 200433 Shanghai, P.R. China
3 Mathematics Department, University of Massachusetts, North Dartmouth, MA 02747, USA
4 Department of Mathematics and SUSTech International Center for Mathematics, Southern University of Science and Technology, 518055 Shenzhen, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 22 August 2019
In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. An artificial stabilizing term is added to the physical model to achieve energy stability, with ETD-based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed 𝓁∞(0,T;𝓁2) error analysis are provided based on the energy method, with a careful estimate of the aliasing error. In addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.
Mathematics Subject Classification: 65M12 / 65M70 / 65Z05
Key words: Epitaxial thin film growth / exponential time differencing / long time energy stability / convergence analysis / second order scheme
© EDP Sciences, SMAI 2020
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