Efficient Linear Schemes with Unconditional Energy Stability for the Phase Field Model of Solid-State Dewetting Problems
Year: 2020
Author: Jie Chen, Zhengkang He, Shuyu Sun, Shimin Guo, Zhangxin Chen
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 3 : pp. 452–468
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1812-m2018-0058
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 3 : pp. 452–468
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Phase field models Solid-state dewetting SAV Energy stability Surface diffusion Finite element method.
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