1. A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection.
- Author
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Chen, Wenbin, Li, Weijia, Luo, Zhiwen, Wang, Cheng, and Wang, Xiaoming
- Subjects
- *
THIN films , *ERROR analysis in mathematics , *COLLOCATION methods , *EVOLUTION equations - 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 Aτ2∂Δ2u∂t A τ 2 ∂ Δ 2 u ∂ t $ A{\tau }^2\frac{\mathrm{\partial }{\Delta }^2u}{\mathrm{\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 𝓁∞(0,T;𝓁2) l ∞ (0 , T ; l 2) $ {\mathcal{l}}^{\mathrm{\infty }}(0,T;{\mathcal{l}}^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. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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