Volume 24, Issue 3
Stabilized Predictor-Corrector Schemes for Gradient Flows with Strong Anisotropic Free Energy

Jie Shen and Jie Xu


Commun. Comput. Phys., 24 (2018), pp. 635-654.

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  • Abstract

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 CahnHilliard equation, the stabilized predictor-corrector scheme is of second-order.

  • History

Published online: 2018-05

  • AMS Subject Headings

65M12, 82C24

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