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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. (English) Zbl 1437.65149

ESAIM, Math. Model. Numer. Anal. 54, No. 3, 727-750 (2020).
Summary: 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 \(A \tau^2 \frac{\partial \Delta^2 u}{\partial t}\) 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.

Cited in 35 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65Z05 Applications to the sciences
35B40 Asymptotic behavior of solutions to PDEs
76A20 Thin fluid films

Keywords:

epitaxial thin film growth; exponential time differencing; long time energy stability; convergence analysis; second order scheme
PDFBibTeX XMLCite
\textit{W. Chen} et al., ESAIM, Math. Model. Numer. Anal. 54, No. 3, 727--750 (2020; Zbl 1437.65149)
Full Text: DOI arXiv

References:

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