Journal
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
Volume 24, Issue 3, Pages 635-654Publisher
GLOBAL SCIENCE PRESS
DOI: 10.4208/cicp.OA-2017-0209
Keywords
Predictor-corrector; anisotropy; Cahn-Hilliard equation; Willmore regularization; degenerate diffusion mobility
Categories
Funding
- NSF [DMS-1620262, DMS-1720442]
- AFOSR [FA9550-16-1-0102]
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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 type 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.
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