@Article{CiCP-24-635,
author = {Jie Shen and Jie Xu},
title = {Stabilized Predictor-Corrector Schemes for Gradient Flows with Strong Anisotropic Free Energy},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {3},
pages = {635--654},
abstract = {<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>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0209},
url = {http://global-sci.org/intro/article_detail/cicp/12274.html}
}