The Development of Discontinuous Galerkin Methods
 Bernardo Cockburn,
 George E. Karniadakis,
 ChiWang Shu
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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 NavierStokes equations, and HamiltonJacobilike equations.
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 Title
 The Development of Discontinuous Galerkin Methods
 Book Title
 Discontinuous Galerkin Methods
 Book Subtitle
 Theory, Computation and Applications
 Book Part
 Part I
 Pages
 pp 350
 Copyright
 2000
 DOI
 10.1007/9783642597213_1
 Print ISBN
 9783642640988
 Online ISBN
 9783642597213
 Series Title
 Lecture Notes in Computational Science and Engineering
 Series Volume
 11
 Series ISSN
 14397358
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors

 Bernardo Cockburn ^{(6)}
 George E. Karniadakis ^{(7)}
 ChiWang Shu ^{(7)}
 Editor Affiliations

 6. School of Mathematics, University of Minnesota
 7. Division of Applied Mathematics, Brown University
 Authors

 Bernardo Cockburn ^{(8)}
 George E. Karniadakis ^{(9)}
 ChiWang Shu ^{(9)}
 Author Affiliations

 8. School of Mathematics, University of Minnesota, Minneapolis, Minnesota, 55455, USA
 9. Division of Applied Mathematics, Brown University, Providence, Rhode Island, 02912, USA
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