Local discontinuous Galerkin methods for the Cahn-Hilliard type equations

被引：123

作者：

Xia, Yinhua

Xu, Yan

Shu, Chi-Wang ^{[1
]}

机构：

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

[2] Univ Twente, Dept Appl Math, NL-7500 AE Enschede, Netherlands

[3] Brown Univ, Div Appl Math, Providence, RI 02912 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2007年 / 227卷 / 01期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Cahn-Hilliard equation; Cahn-Hilliard system; local discontinuous Galerkin methods; stability;

D O I：

10.1016/j.jcp.2007.08.001

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we develop local discontinuous Galerkin (LDG) methods for the fourth order nonlinear Cahn-Hilliar 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 if numerical results illustrate the accuracy and capability of the methods. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：472 / 491

页数：20

共 37 条

[1] Unified analysis of discontinuous Galerkin methods for elliptic problems [J].

Arnold, DN ;

Brezzi, F ;

Cockburn, B ;

Marini, LD .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779

[2] Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy [J].

Barrett, JW ;

Blowey, JF .

NUMERISCHE MATHEMATIK, 1997, 77 (01) :1-34

[3] Finite element approximation of the Cahn-Hilliard equation with degenerate mobility [J].

Barrett, JW ;

Blowey, JF ;

Garcke, H .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 37 (01) :286-318

[4] On fully practical finite element approximations of degenerate Cahn-Hilliard systems [J].

Barrett, JW ;

Blowey, JF ;

Garcke, H .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2001, 35 (04) :713-748

[5] A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations [J].

Bassi, F ;

Rebay, S .

JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 131 (02) :267-279

[6]

Blowey J. F., 1992, Euro. J. Appl. Math., V3, P147, DOI DOI 10.1017/S0956792500000759

[7] Numerical analysis of a model for phase separation of a multi-component alloy [J].

Blowey, JF ;

Copetti, MIM ;

Elliott, CM .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1996, 16 (01) :111-139

[8] FREE ENERGY OF A NONUNIFORM SYSTEM .1. INTERFACIAL FREE ENERGY [J].

CAHN, JW ;

HILLIARD, JE .

JOURNAL OF CHEMICAL PHYSICS, 1958, 28 (02) :258-267

[9] A discontinuous Galerkin method for the Cahn-Hilliard equation [J].

Choo S.M. ;

Lee Y.J. .

Journal of Applied Mathematics and Computing, 2005, 18 (1-2) :113-126

[10] The local discontinuous Galerkin method for time-dependent convection-diffusion systems [J].

Cockburn, B ;

Shu, CW .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (06) :2440-2463

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