Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin Methods

Bernardo Cockburn (1) , Daniele Di Pietro (2) , Alexandre Ern (3)

1 UMN-MATH - School of Mathematics
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

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, delicate 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.

Mots clés: hybridizable discontinuous Galerkin; hybrid high-order; variable diffusion

Domaines: Analyse numérique [math.NA]

Bernardo Cockburn, Daniele Di Pietro, Alexandre Ern. Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin Methods. ESAIM: Mathematical Modelling and Numerical Analysis, 2016, Polyhedral discretization for PDE, 50 (3), pp.635-650. ⟨10.1051/m2an/2015051⟩. ⟨hal-01115318v2⟩