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The Effect of the Least Square Procedure for Discontinuous Galerkin Methods for Hamilton-Jacobi Equations

  • Changqing Hu
  • Olga Lepsky
  • Chi-Wang Shu
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)

Abstract

In this presentation, we perform further investigation on the least square procedure used in the discontinuous Galerkin methods developed in [2] and [3] for the two-dimensional Hamilton-Jacobi equations. The focus of this presentation will be upon the influence of this least square procedure to the accuracy and stability of the numerical results. We will show through numerical examples that the procedure is crucial for the success of the discontinuous Galerkin methods developed in [2] and [3], especially for high order methods. New test cases using P 4 polynomials, which are at least fourth order and often fifth order accurate, are shown, in addition to the P 2 and P 3 cases presented in [2] and [3]. This addition is non-trivial as the least square procedure plays a more significant role for the P 4 case.

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References

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    B. Cockburn, S. Hou and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws IV: the multidimensional case, Math. Comp., v54 (1990), pp. 545–581.MathSciNetzbMATHGoogle Scholar
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    C. Hu and C.-W. Shu, Discontinuous Galerkin finite element method for Hamilton-Jacobi equations,To appear in SIAM J. Sci. Comput.Google Scholar
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    O. Lepsky, C. Hu and C.-W. Shu, Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations,To appear in Appl. Numer. Math.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Changqing Hu
    • 1
  • Olga Lepsky
    • 2
  • Chi-Wang Shu
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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