Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods

• Published in: ESAIM. Mathematical modelling and numerical analysis Vol. 50; no. 3; pp. 635 - 650
• Main Authors: Cockburn, Bernardo, Di Pietro, Daniele A., Ern, Alexandre
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.05.2016; Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP
• Series: Polyhedral discretization for PDE
• Subjects: 65N08; 65N30; Construction methods; Galerkin method; hybrid high-order; Hybridizable discontinuous Galerkin; Mathematical models; Mathematics; Methods; Numerical Analysis; variable diffusion problems; hybrid high-order; variable diffusion; hybridizable discontinuous Galerkin
• ISSN: 0764-583X; 2822-7840; 1290-3841; 2804-7214
• DOI: 10.1051/m2an/2015051

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.