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Volume 38, Issue 3
Efficient Linear Schemes with Unconditional Energy Stability for the Phase Field Model of Solid-State Dewetting Problems

Jie Chen, Zhengkang He, Shuyu Sun, Shimin Guo & Zhangxin Chen

DOI: 10.4208/jcm.1812-m2018-0058

J. Comp. Math., 38 (2020), pp. 452-468.

Published online: 2020-03

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  • 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.

  • Keywords

Phase field models, Solid-state dewetting, SAV, Energy stability, Surface diffusion, Finite element method.

  • AMS Subject Headings

65N38, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

chenjiexjtu@mail.xjtu.edu.cn (Jie Chen)

hzk2abc@163.com (Zhengkang He)

shuyu.sun@kaust.edu.sa (Shuyu Sun)

shiminguo@xjtu.edu.cn (Shimin Guo)

zhachen@ucalgary.ca (Zhangxin Chen)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-452, author = {Chen , JieHe , ZhengkangSun , ShuyuGuo , Shimin and Chen , Zhangxin}, title = {Efficient Linear Schemes with Unconditional Energy Stability for the Phase Field Model of Solid-State Dewetting Problems}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1812-m2018-0058}, url = {http://global-sci.org/intro/article_detail/jcm/15795.html} }
TY - JOUR T1 - Efficient Linear Schemes with Unconditional Energy Stability for the Phase Field Model of Solid-State Dewetting Problems AU - Chen , Jie AU - He , Zhengkang AU - Sun , Shuyu AU - Guo , Shimin AU - Chen , Zhangxin JO - Journal of Computational Mathematics VL - 3 SP - 452 EP - 468 PY - 2020 DA - 2020/03 SN - 38 DO - http://doi.org/10.4208/jcm.1812-m2018-0058 UR - https://global-sci.org/intro/article_detail/jcm/15795.html KW - Phase field models, Solid-state dewetting, SAV, Energy stability, Surface diffusion, Finite element method. AB -

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.

Chen , JieHe , ZhengkangSun , ShuyuGuo , Shimin and Chen , Zhangxin. (2020). Efficient Linear Schemes with Unconditional Energy Stability for the Phase Field Model of Solid-State Dewetting Problems. Journal of Computational Mathematics. 38 (3). 452-468. doi:10.4208/jcm.1812-m2018-0058
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