摘要
In this paper,we consider the application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system.The method in this paper extends the local discontinuous Galerkin method in[10]to the more general application system which is coupled with the Allen-Cahn and Cahn-Hilliard equations.Similar energy stability result as that in[10]is presented.Numerical results for the nonlinear problems which include the Allen-Cahn/Cahn-Hilliard system for one-dimensional and two-dimensional cases demonstrate the accuracy and capability of the numerical method.
基金
The research of the first author is supported in part byNSFC grant 10601055
The research of the second author is supported by NSFC grant 10601055
The research of the third author is supported in part by NSFC grant 10671190 during his visit to the Department of Mathematics,University of Science and Technology of China,Hefei,Anhui 230026,P.R.China
Additional support is provided by NSF grant DMS-0510345。
