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 - <p style="text-align: justify;">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 &quot;scalar auxiliary variable&quot; (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.</p>