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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2007
Accession Number
ADA464873

Entities

People

  • Chi-Wang Shu
  • Yan Xu
  • Yinhua Xia

Organizations

  • University of Science and Technology of China

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Alloys
  • Applied Mathematics
  • Binary Alloys
  • Boundaries
  • Differential Equations
  • Equations
  • Free Energy
  • Galerkin Method
  • Mathematics
  • Navier Stokes Equations
  • Phase Separation
  • Schrodinger Equation
  • Simulations
  • Spinodal Decomposition
  • Two Dimensional
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)