Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods
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 identi...
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| Published in | ESAIM. Mathematical modelling and numerical analysis Vol. 50; no. 3; pp. 635 - 650 |
|---|---|
| Main Authors | , , |
| 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 | |
| Online Access | Get full text |
| ISSN | 0764-583X 2822-7840 1290-3841 2804-7214 |
| DOI | 10.1051/m2an/2015051 |
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| 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. |
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| AbstractList | 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. 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. |
| Author | Ern, Alexandre Di Pietro, Daniele A. Cockburn, Bernardo |
| Author_xml | – sequence: 1 givenname: Bernardo surname: Cockburn fullname: Cockburn, Bernardo organization: School of Mathematics, University of Minnesota, Minneapolis, USA – sequence: 2 givenname: Daniele A. surname: Di Pietro fullname: Di Pietro, Daniele A. organization: University of Montpellier, Institut Montpelliérain Alexander Grothendieck, 34095 Montpellier, France – sequence: 3 givenname: Alexandre surname: Ern fullname: Ern, Alexandre organization: University Paris-Est, CERMICS (ENPC), 77455 Marne-la-Vallée cedex 2, France |
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| Cites_doi | 10.1007/978-3-642-22980-0 10.1016/j.crma.2014.10.013 10.1007/978-3-319-02663-3 10.1016/j.jcp.2014.04.021 10.1016/0377-0427(94)90046-9 10.1016/j.cma.2014.09.009 10.1051/m2an/2013104 10.1016/j.crma.2014.12.009 10.1007/s10915-015-0024-5 10.1016/j.compfluid.2013.11.017 10.1007/s10915-014-9962-6 10.1002/nme.2646 |
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| Title | Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods |
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