Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods

Bernardo Cockburn, Daniele A. Di Pietro, Alexandre Ern

Research output: Contribution to journalArticle

55 Citations (Scopus)

Abstract

We build a bridge between the hybrid high-order (HHO) and the hybridizable discontinuous Galerkin (HDG) methods in the setting of a model diffusion problem. First, we briefly recall the construction of HHO methods and derive some new variants. Then, by casting the HHO method in mixed form, we identify the numerical flux so that the HHO method can be compared to HDG methods. In turn, the incorporation of the HHO method into the HDG framework brings up new, efficient choices of the local spaces and a new, subtle construction of the numerical flux ensuring optimal orders of convergence on meshes made of general shape-regular polyhedral elements. Numerical experiments comparing two of these methods are shown.

Original languageEnglish (US)
Pages (from-to)635-650
Number of pages16
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume50
Issue number3
DOIs
StatePublished - May 1 2016

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High-order Methods
Discontinuous Galerkin Method
Galerkin methods
Hybrid Method
Higher Order
Fluxes
Casting
Discontinuous Galerkin
Diffusion Problem
Order of Convergence
Experiments
Numerical Experiment
Mesh
Model

Keywords

  • Hybrid high-order
  • Hybridizable discontinuous Galerkin
  • Variable diffusion problems

Cite this

Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. / Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre.

In: ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 50, No. 3, 01.05.2016, p. 635-650.

Research output: Contribution to journalArticle

Cockburn, Bernardo ; Di Pietro, Daniele A. ; Ern, Alexandre. / Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. In: ESAIM: Mathematical Modelling and Numerical Analysis. 2016 ; Vol. 50, No. 3. pp. 635-650.
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