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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 |
Issue Date: | 2018 | Source: | Mathematics of computation, 2018, v. 87, p. 1859-1885 | 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. | Keywords: | Energy stability Error estimates Exponential time differencing Fourier collocation Linear convex splitting Thin film growth |
Publisher: | American Mathematical Society | Journal: | Mathematics of computation | ISSN: | 0025-5718 | DOI: | 10.1090/mcom/3262 | Rights: | © Copyright 2017 American Mathematical Society This is a preliminary PDF of the author-produced manuscript that has been peer-reviewed and accepted for publication. The definitive publisher authenticated version is available online at https://doi.org/10.1090/mcom/3262 |
Appears in Collections: | Journal/Magazine Article |
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File | Description | Size | Format | |
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Ju_Energy_Stability_Error.pdf | Pre-Published version | 1.33 MB | Adobe PDF | View/Open |
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