Local discontinuous Galerkin methods for the Cahn-Hilliard type equations

Authors:
Yinhua Xia;Yan Xu;Chi-Wang Shu
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China;Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

In this paper, we develop local discontinuous Galerkin (LDG) methods for the fourth order nonlinear Cahn-Hilliard equation and system. The energy stability of the LDG methods is proved for the general nonlinear case. Numerical examples for the Cahn-Hilliard equation and the Cahn-Hilliard system in one and two dimensions are presented and the numerical results illustrate the accuracy and capability of the methods.