HDG Methods for Hyperbolic Problems

B. Cockburn, N. C. Nguyen, J. Peraire

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Scopus citations

Abstract

We give a short overview of the development of the so-called hybridizable discontinuous Galerkin methods for hyperbolic problems. We describe the methods, discuss their main features and display numerical results which illustrate their performance. We do this in the framework of wave propagation problems. In particular, we show that these methods are amenable to static condensation, and hence to efficient implementation, both for time-dependent (with implicit time-marching schemes) and for time-harmonic problems; we also show that they can be used with explicit time-marching schemes. We discuss an unexpected, recently uncovered superconvergence property and introduce a new postprocessing for time-harmonic Maxwell's equations. We end by providing bibliographical notes.

Original languageEnglish (US)
Title of host publicationHandbook of Numerical Analysis
PublisherElsevier B.V.
Pages173-197
Number of pages25
DOIs
StatePublished - Dec 1 2016

Publication series

NameHandbook of Numerical Analysis
Volume17
ISSN (Print)1570-8659

Bibliographical note

Funding Information:
The authors would like to thank Rémi Abgrall and Chi-Wang Shu for the invitation to write this chapter. B.C. was supported in part by the National Science Foundation (Grant DMS-1522657) and by the University of Minnesota Supercomputing Institute. N.C.N. and J.P. were supported in part by the Singapore-MIT Alliance.

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

  • Discontinuous Galerkin methods
  • Hybridization
  • Hyperbolic problems

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