Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods

¹ School of Mathematics, University of Minnesota, Minneapolis, USA
cockburn@math.umn.edu
² University of Montpellier, Institut Montpelliérain Alexander Grothendieck, 34095 Montpellier, France
daniele.di-pietro@umontpellier.fr
³ University Paris-Est, CERMICS (ENPC), 77455 Marne-la-Vallée cedex 2, France
ern@cermics.enpc.fr

Received: 10 February 2015
Revised: 4 July 2015

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.