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

Published online by Cambridge University Press:  03 June 2015

Feng Chen  and
Jie Shen
Feng Chen*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957, USA
Jie Shen*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957, USA
*
Email:feng_chen_1@brown.edu
Corresponding author.Email:shen@math.purdue.edu
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Abstract

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.

Keywords

65N3565M1235K55Spectral-Galerkinphase-fieldanisotropicCahn-Hilliardstabilizationcoupled elliptic equations
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 5 , May 2013 , pp. 1189 - 1208
Copyright
Copyright © Global Science Press Limited 2013

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