Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/77874
Title: Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection
Authors: Ju, L
Li, X
Qiao, Z 
Zhang, H
Keywords: Energy stability
Error estimates
Exponential time differencing
Fourier collocation
Linear convex splitting
Thin film growth
Issue Date: 2018
Publisher: American Mathematical Society
Source: Mathematics of computation, 2018, v. 87, no. 312, p. 1859-1885 How to cite?
Journal: Mathematics of computation 
Abstract: In this paper, we propose a class of exponential time differencing (ETD) schemes for solving the epitaxial growth model without slope selection. A linear convex splitting is first applied to the energy functional of the model, and then Fourier collocation and ETD-based multistep approximations are used respectively for spatial discretization and time integration of the corresponding gradient flow equation. Energy stabilities and error estimates of the first and second order ETD schemes are rigorously established in the fully discrete sense. We also numerically demonstrate the accuracy of the proposed schemes and simulate the coarsening dynamics with small diffusion coefficients. The results show the logarithm law for the energy decay and the power laws for growth of the surface roughness and the mound width, which are consistent with the existing theories in the literature.
URI: http://hdl.handle.net/10397/77874
ISSN: 0025-5718
DOI: 10.1090/mcom/3262
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