TY - JOUR
T1 - Stabilized Predictor-Corrector Schemes for Gradient Flows with Strong Anisotropic Free Energy
AU - Jie Shen & Jie Xu
JO - Communications in Computational Physics
VL - 3
SP - 635
EP - 654
PY - 2018
DA - 2018/05
SN - 24
DO - http://doi.org/10.4208/cicp.OA-2017-0209
UR - https://global-sci.org/intro/article_detail/cicp/12274.html
KW - Predictor-corrector, anisotropy, Cahn-Hilliard equation, Willmore regularization, degenerate diffusion mobility.
AB - <p style="text-align: justify;">Gradient flows with strong anisotropic free energy are difficult to deal with
numerically with existing approaches. We propose a stabilized predictor-corrector approach
to construct schemes which are second-order accurate, easy to implement, and
maintain the stability of first-order stabilized schemes. We apply the new approach to
three different types of gradient flows with strong anisotropic free energy: anisotropic
diffusion equation, anisotropic Cahn-Hilliard equation, and Cahn-Hilliard equation
with degenerate diffusion mobility. Numerical results are presented to show that the
stabilized predictor-corrector schemes are second-order accurate, unconditionally stable
for the first two equations, and allow larger time step than the first-order stabilized
scheme for the last equation. We also prove rigorously that, for the isotropic Cahn-Hilliard
equation, the stabilized predictor-corrector scheme is of second-order.</p>