The hybridizable discontinuous Galerkin methods

Bernardo Cockburn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations

Abstract

In this paper, we present and discuss the so-called hybridizable discontinuous Galerkin (HDG) methods. The discontinuous Galerkin (DG) methods were originally devised for numerically solving linear and then nonlinear hyperbolic problems. Their success prompted their extension to the compressible Navier-Stokes equations - and hence to second-order elliptic equations. The clash between the DG methods and decades-old, well-established finite element methods resulted in the introduction of the HDG methods. The HDG methods can be implemented more efficiently and are more accurate than all previously known DG methods; they represent a competitive alternative to the well established finite element methods. Here we show how to devise and implement the HDG methods, argue why they work so well and prove optimal convergence properties in the framework of diffusion and incompressible flow problems. We end by briefly describing extensions to other continuum mechanics and fluid dynamics problems.

Original languageEnglish (US)
Title of host publicationProceedings of the International Congress of Mathematicians 2010, ICM 2010
Pages2749-2775
Number of pages27
StatePublished - Dec 1 2010
EventInternational Congress of Mathematicians 2010, ICM 2010 - Hyderabad, India
Duration: Aug 19 2010Aug 27 2010

Publication series

NameProceedings of the International Congress of Mathematicians 2010, ICM 2010

Other

OtherInternational Congress of Mathematicians 2010, ICM 2010
CountryIndia
CityHyderabad
Period8/19/108/27/10

Keywords

  • Convection
  • Diffusion
  • Discontinuous Galerkin methods
  • Finite element methods
  • Incompressible fluid flow
  • Mixed methods

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