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.
DOI : 10.1051/m2an/2015051
Mots-clés : Hybridizable discontinuous Galerkin, hybrid high-order, variable diffusion problems
@article{M2AN_2016__50_3_635_0,
author = {Cockburn, Bernardo and Di Pietro, Daniele A. and Ern, Alexandre},
title = {Bridging the hybrid high-order and hybridizable discontinuous {Galerkin} methods},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {635--650},
publisher = {EDP-Sciences},
volume = {50},
number = {3},
year = {2016},
doi = {10.1051/m2an/2015051},
zbl = {1341.65045},
mrnumber = {3507267},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2015051/}
}
TY - JOUR AU - Cockburn, Bernardo AU - Di Pietro, Daniele A. AU - Ern, Alexandre TI - Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 635 EP - 650 VL - 50 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2015051/ DO - 10.1051/m2an/2015051 LA - en ID - M2AN_2016__50_3_635_0 ER -
%0 Journal Article %A Cockburn, Bernardo %A Di Pietro, Daniele A. %A Ern, Alexandre %T Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 635-650 %V 50 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2015051/ %R 10.1051/m2an/2015051 %G en %F M2AN_2016__50_3_635_0
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre. Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 635-650. doi : 10.1051/m2an/2015051. http://archive.numdam.org/articles/10.1051/m2an/2015051/
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