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Discontinuous Galerkin Methods pp 3–50Cite as

The Development of Discontinuous Galerkin Methods

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Part of the book series: Lecture Notes in Computational Science and Engineering ((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.

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  1. School of Mathematics, University of Minnesota, Minneapolis, Minnesota, 55455, USA

    Bernardo Cockburn

  2. Division of Applied Mathematics, Brown University, Providence, Rhode Island, 02912, USA

    George E. Karniadakis & Chi-Wang Shu

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  1. School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN, 55455, USA

    Bernardo Cockburn

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    George E. Karniadakis  & Chi-Wang Shu  & 

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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. https://doi.org/10.1007/978-3-642-59721-3_1

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