A Local Discontinuous Galerkin Method for the Camassa-Holm Equation

Abstract

In this paper, we develop, analyze and test a local discontinuous Galerkin (LDG) method for solving the Camassa-Holm equation which contains nonlinear high order derivatives. The LDG method has the flexibility for arbitrary h and p adaptivity. We prove the L2 stability for general solutions and give a detailed error estimate for smooth solutions, and provide numerical simulation results for different types of solutions of the nonlinear Camassa-Holm equation to illustrate the accuracy and capability of the LDG method.

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Document Details

Document Type
Technical Report
Publication Date
Jan 10, 2007
Accession Number
ADA464872

Entities

People

  • Chi-Wang Shu
  • Yan Xu

Organizations

  • University of Twente

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Accuracy
  • Applied Mathematics
  • Boundaries
  • Computations
  • Differential Equations
  • Equations
  • Error Analysis
  • Errors
  • Galerkin Method
  • Inequalities
  • Mathematics
  • Notation
  • Partial Differential Equations
  • Polynomials
  • Runge Kutta Method
  • Traveling Waves
  • Wave Equations

Fields of Study

  • Mathematics

Readers

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