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 language||English (US)|
|Title of host publication||Handbook of Numerical Analysis|
|Number of pages||25|
|State||Published - Dec 1 2016|
|Name||Handbook of Numerical Analysis|
Bibliographical noteFunding 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.
© 2016 Elsevier B.V.
- Discontinuous Galerkin methods
- Hyperbolic problems