Geodesic
A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 3, pp. 727-750.

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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 ∂Δ 2 u ∂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;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.

DOI : 10.1051/m2an/2019054
Classification : 65M12, 65M70, 65Z05
Keywords: Epitaxial thin film growth, exponential time differencing, long time energy stability, convergence analysis, second order scheme 
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     author = {Chen, Wenbin and Li, Weijia and Luo, Zhiwen and Wang, Cheng and Wang, Xiaoming},
     title = {A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {727--750},
     publisher = {EDP-Sciences},
     volume = {54},
     number = {3},
     year = {2020},
     doi = {10.1051/m2an/2019054},
     mrnumber = {4080786},
     zbl = {1437.65149},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2019054/}
}
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Chen, Wenbin; Li, Weijia; Luo, Zhiwen; Wang, Cheng; Wang, Xiaoming. A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 3, pp. 727-750. doi : 10.1051/m2an/2019054. http://geodesic.mathdoc.fr/articles/10.1051/m2an/2019054/

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