Local discontinuous Galerkin methods for the Cahn–Hilliard type equations

Yinhua Xia; Y. Xu; Chi-Wang Shu

doi:10.1016/j.jcp.2007.08.001

Local discontinuous Galerkin methods for the Cahn–Hilliard type equations

Yinhua Xia, Y. Xu, Chi-Wang Shu

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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.

Original language	Undefined
Pages (from-to)	472-491
Journal	Journal of computational physics
Volume	227
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2007.08.001
Publication status	Published - 2007

Keywords

Cahn–Hilliard equation
Stability
IR-78841
Local discontinuous Galerkin methods
Cahn–Hilliard system

Access to Document

10.1016/j.jcp.2007.08.001

Cite this

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title = "Local discontinuous Galerkin methods for the Cahn–Hilliard type equations",

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.",

keywords = "Cahn–Hilliard equation, Stability, IR-78841, Local discontinuous Galerkin methods, Cahn–Hilliard system",

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T1 - Local discontinuous Galerkin methods for the Cahn–Hilliard type equations

AU - Xia, Yinhua

AU - Xu, Y.

AU - Shu, Chi-Wang

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Cahn–Hilliard equation

KW - Stability

KW - IR-78841

KW - Local discontinuous Galerkin methods

KW - Cahn–Hilliard system

U2 - 10.1016/j.jcp.2007.08.001

DO - 10.1016/j.jcp.2007.08.001

M3 - Article

SN - 0021-9991

VL - 227

SP - 472

EP - 491

JO - Journal of computational physics

JF - Journal of computational physics

IS - 1

ER -