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.
Email: firstname.lastname@example.org (F. Chen), email@example.com (J. Shen)