Author:
Chen Wenbin,Li Weijia,Luo Zhiwen,Wang Cheng,Wang Xiaoming
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 $ 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) 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.
Subject
Applied Mathematics,Modeling and Simulation,Numerical Analysis,Analysis,Computational Mathematics
Cited by
37 articles.
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