The hybrid high-order method for polytopal meshes

DA Di Pietro, J Droniou - Number 19 in Modeling, Simulation and …, 2020 - Springer
Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

High order exactly divergence-free hybrid discontinuous Galerkin methods for unsteady incompressible flows

C Lehrenfeld, J Schöberl - Computer Methods in Applied Mechanics and …, 2016 - Elsevier
In this paper we present an efficient discretization method for the solution of the unsteady
incompressible Navier–Stokes equations based on a high order (Hybrid) Discontinuous …

An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier–Stokes equations

NC Nguyen, J Peraire, B Cockburn - Journal of Computational Physics, 2011 - Elsevier
We present an implicit high-order hybridizable discontinuous Galerkin method for the steady-
state and time-dependent incompressible Navier–Stokes equations. The method is devised …

Devising HDG methods for Stokes flow: an overview

B Cockburn, K Shi - Computers & Fluids, 2014 - Elsevier
We provide a short overview of our recent work on the devising of hybridizable
discontinuous Galerkin (HDG) methods for the Stokes equations of incompressible flow …

Static condensation, hybridization, and the devising of the HDG methods

B Cockburn - Building bridges: connections and challenges in …, 2016 - Springer
In this paper, we review and refine the main ideas for devising the so-called hybridizable
discontinuous Galerkin (HDG) methods; we do that in the framework of steady-state diffusion …

Analysis of HDG methods for Stokes flow

B Cockburn, J Gopalakrishnan, N Nguyen… - Mathematics of …, 2011 - ams.org
In this paper, we analyze a hybridizable discontinuous Galerkin method for numerically
solving the Stokes equations. The method uses polynomials of degree $ k $ for all the …

Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics

NC Nguyen, J Peraire - Journal of Computational Physics, 2012 - Elsevier
We present hybridizable discontinuous Galerkin methods for solving steady and time-
dependent partial differential equations (PDEs) in continuum mechanics. The essential …

High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics

NC Nguyen, J Peraire, B Cockburn - Journal of Computational Physics, 2011 - Elsevier
We present a class of hybridizable discontinuous Galerkin (HDG) methods for the numerical
simulation of wave phenomena in acoustics and elastodynamics. The methods are fully …

[HTML][HTML] A hybridizable discontinuous Galerkin method for the Navier–Stokes equations with pointwise divergence-free velocity field

S Rhebergen, GN Wells - Journal of Scientific Computing, 2018 - Springer
We introduce a hybridizable discontinuous Galerkin method for the incompressible Navier–
Stokes equations for which the approximate velocity field is pointwise divergence-free. The …

Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations

NC Nguyen, J Peraire, B Cockburn - Journal of Computational Physics, 2011 - Elsevier
We present two hybridizable discontinuous Galerkin (HDG) methods for the numerical
solution of the time-harmonic Maxwell's equations. The first HDG method explicitly enforces …