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 …

Hybridizable discontinuous Galerkin methods for second-order elliptic problems: overview, a new result and open problems

B Cockburn - Japan Journal of Industrial and Applied Mathematics, 2023‏ - Springer
We describe, in the framework of steady-state diffusion problems, the history of the
development of the so-called hybridizable discontinuous Galerkin (HDG) methods, since …

A unified study of continuous and discontinuous Galerkin methods

Q Hong, F Wang, S Wu, J Xu - Science China Mathematics, 2019‏ - Springer
A unified study is presented in this paper for the design and analysis of different finite
element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs …

Hybridisable discontinuous Galerkin formulation of compressible flows

J Vila-Pérez, M Giacomini, R Sevilla… - Archives of Computational …, 2021‏ - Springer
This work presents a review of high-order hybridisable discontinuous Galerkin (HDG)
methods in the context of compressible flows. Moreover, an original unified framework for …

Hybrid high-order and weak Galerkin methods for the biharmonic problem

Z Dong, A Ern - SIAM Journal on Numerical Analysis, 2022‏ - SIAM
We devise and analyze two hybrid high-order (HHO) methods for the numerical
approximation of the biharmonic problem. The methods support polyhedral meshes, rely on …

Discontinuous G alerkin Methods for Computational Fluid Dynamics

B Cockburn - Encyclopedia of computational mechanics, 2004‏ - Wiley Online Library
The discontinuous Galerkin methods are locally conservative, high‐order accurate, and
robust methods that can easily handle elements of arbitrary shapes, irregular triangulations …

Stormer-Numerov HDG methods for acoustic waves

B Cockburn, Z Fu, A Hungria, L Ji, MA Sánchez… - Journal of Scientific …, 2018‏ - Springer
We introduce and analyze the first energy-conservative hybridizable discontinuous Galerkin
method for the semidiscretization in space of the acoustic wave equation. We prove optimal …

[HTML][HTML] Implementation of discontinuous skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming

M Cicuttin, DA Di Pietro, A Ern - Journal of Computational and Applied …, 2018‏ - Elsevier
Discontinuous Skeletal methods approximate the solution of boundary-value problems by
attaching discrete unknowns to mesh faces (hence the term skeletal) while allowing these …

Tutorial on Hybridizable Discontinuous Galerkin (HDG) formulation for incompressible flow problems

M Giacomini, R Sevilla, A Huerta - … numerical methods for solids and fluids, 2020‏ - Springer
A hybridizable discontinuous Galerkin (HDG) formulation of the linearized incompressible
Navier-Stokes equations, known as Oseen equations, is presented. The Cauchy stress …

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

M Giacomini, R Sevilla, A Huerta - Archives of Computational Methods in …, 2021‏ - Springer
This paper presents HDGlab, an open source MATLAB implementation of the hybridisable
discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of …