TY - JOUR
T1 - Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods
AU - Cockburn, Bernardo
AU - Di Pietro, Daniele A.
AU - Ern, Alexandre
N1 - Publisher Copyright:
© 2016 EDP Sciences, SMAI.
PY - 2016/5/1
Y1 - 2016/5/1
N2 - 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.
AB - 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.
KW - Hybrid high-order
KW - Hybridizable discontinuous Galerkin
KW - Variable diffusion problems
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U2 - 10.1051/m2an/2015051
DO - 10.1051/m2an/2015051
M3 - Article
AN - SCOPUS:84971405727
SN - 2822-7840
VL - 50
SP - 635
EP - 650
JO - ESAIM: Mathematical Modelling and Numerical Analysis
JF - ESAIM: Mathematical Modelling and Numerical Analysis
IS - 3
ER -