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Journal of Scientific Computing

, Volume 81, Issue 3, pp 1509–1526 | Cite as

Discontinuous Galerkin Difference Methods for Symmetric Hyperbolic Systems

  • T. HagstromEmail author
  • J. W. Banks
  • B. B. Buckner
  • K. Juhnke
Article
  • 63 Downloads

Abstract

We develop dissipative, energy-stable difference methods for linear first-order hyperbolic systems by applying an upwind, discontinuous Galerkin construction of derivative matrices to a space of discontinuous piecewise polynomials on a structured mesh. The space is spanned by translates of a function spanning multiple cells, yielding a class of implicit difference formulas of arbitrary order. We examine the properties of the method, including the scaling of the derivative operator with method order, and demonstrate its accuracy for problems in one and two space dimensions.

Keywords

Difference methods Galerkin methods Hyperbolic systems 

Mathematics Subject Classification

65M60 65M06 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • T. Hagstrom
    • 1
    Email author
  • J. W. Banks
    • 2
  • B. B. Buckner
    • 2
  • K. Juhnke
    • 3
  1. 1.Department of MathematicsSouthern Methodist UniversityDallasUSA
  2. 2.Rensselaer Polytechnic InstituteTroyUSA
  3. 3.Bethel CollegeNorth NewtonUSA

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