Stabilized Predictor-Corrector Schemes for Gradient Flows with Strong Anisotropic Free Energy (Communications in Computational Physics, 2018)
Gradient flows with strong anisotropic free energy are difficult to deal withnumerically with existing approaches. We propose a stabilized predictor-corrector approachto construct schemes which are second-order accurate, easy to implement, andmaintain the stability of first-order stabilized schemes. We apply the new approach tothree different types of gradient flows with strong anisotropic free energy: anisotropicdiffusion equation, anisotropic Cahn-Hilliard equation, and Cahn-Hilliard equationwith degenerate diffusion mobility. Numerical results are presented to show that thestabilized predictor-corrector schemes are second-order accurate, unconditionally stablefor the first two equations, and allow larger time step than the first-order stabilizedscheme for the last equation. We also prove rigorously that, for the isotropic Cahn-Hilliardequation, the stabilized predictor-corrector scheme is of second-order.
Keywords: Predictor-corrector; anisotropy; Cahn-Hilliard equation; Willmore regularization; degenerate diffusion mobility.