Abstract
In this paper, we study linearly first and second order in time, uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel “scalar auxiliary variable” (SAV) approach, a new developed efficient and accurate method for a large class of gradient flows. The schemes are based on the first order Euler method and the second order backward differential formulas (BDF2) for time discretization, and finite element methods for space discretization. The proposed schemes are proved to be unconditionally stable and the discrete equations are uniquely solvable for all time steps. Various numerical experiments are presented to validate the stability and accuracy of the proposed schemes.
Original language | English (US) |
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Pages (from-to) | 452-468 |
Number of pages | 17 |
Journal | Journal of Computational Mathematics |
Volume | 38 |
Issue number | 3 |
DOIs | |
State | Published - Mar 24 2020 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): BAS/1/1351-01-01
Acknowledgements: The work is supported by the National Natural Science Foundation of China (No.11401467), China Postdoctoral Science Foundation (No. 2013M542334. and No. 2015T81012), and Natural Science Foundation of Shaanxi Province (No. 2015JQ1012). The work is also supported in part by funding from King Abdullah University of Science and Technology (KAUST) through the grant BAS/1/1351-01-01.