Commun. Comput. Phys., 13 (2013), pp. 1189-1208.

Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn-Hilliard Systems

Feng Chen 1, Jie Shen 1*

1 Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957, USA.

Received 10 November 2011; Accepted (in revised version) 11 May 2012
Available online 8 October 2012


We develop in this paper efficient and robust numerical methods for solving anisotropic Cahn-Hilliard systems. We construct energy stable schemes for the time discretization of the highly nonlinear anisotropic Cahn-Hilliard systems by using a stabilization technique. At each time step, these schemes lead to a sequence of linear coupled elliptic equations with constant coefficients that can be efficiently solved by using a spectral-Galerkin method. We present numerical results that are consistent with earlier work on this topic, and also carry out various simulations, such as the linear bi-Laplacian regularization and the nonlinear Willmore regularization, to demonstrate the efficiency and robustness of the new schemes.

AMS subject classifications: 65N35, 65M12, 35K55

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Key words: Spectral-Galerkin, phase-field, anisotropic, Cahn-Hilliard, stabilization, coupled elliptic equations.

*Corresponding author.
Email: (F. Chen), (J. Shen)

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