The Development of Discontinuous Galerkin Methods

  • Bernardo Cockburn
  • George E. Karniadakis
  • Chi-Wang Shu
Conference paper

DOI: 10.1007/978-3-642-59721-3_1

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)
Cite this paper as:
Cockburn B., Karniadakis G.E., Shu CW. (2000) The Development of Discontinuous Galerkin Methods. In: Cockburn B., Karniadakis G.E., Shu CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg

Abstract

In this paper, we present an overview of the evolution of the discontinuous Galerkin methods since their introduction in 1973 by Reed and Hill, in the framework of neutron transport, until their most recent developments. We show how these methods made their way into the main stream of computational fluid dynamics and how they are quickly finding use in a wide variety of applications. We review the theoretical and algorithmic aspects of these methods as well as their applications to equations including nonlinear conservation laws, the compressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Bernardo Cockburn
    • 1
  • George E. Karniadakis
    • 2
  • Chi-Wang Shu
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

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