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The Development of Discontinuous Galerkin Methods

  • Bernardo Cockburn
  • George E. Karniadakis
  • Chi-Wang Shu
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)

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.

Keywords

Posteriori Error Discontinuous Galerkin Discontinuous Galerkin Method Numerical Flux Hyperbolic Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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