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arXiv · 1907.02234

A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection

Wenbin Chen·Weijia Li·Zhiwen Luo·Cheng Wang·Xiaoming Wang
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Abstract

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 $Aτ^2\frac{\partialΔ^2 u}{\partial t}$ 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 $\ell^{\infty}(0,T; \ell^2)$ 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.

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Wenbin Chen, Weijia Li, Zhiwen Luo, Cheng Wang, Xiaoming Wang. 2019-07-04. A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection. https://arxiv.org/abs/1907.02234

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