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 discrete-ordinates variational nodal method for heterogeneous neutron Boltzmann transport problems

Q Sun, X Liu, X Chai, H He, T Zhang - Computers & Mathematics with …, 2024 - Elsevier
This study introduces an unstructured variational nodal method (UVNM-S N), also
recognized as the hybridized discontinuous Galerkin (HDG) method, for solving …

An adaptive high-order transient algorithm to solve large-scale anisotropic Maxwell's equations

Q Zhan, Y Wang, Y Fang, Q Ren, S Yang… - … on Antennas and …, 2021 - ieeexplore.ieee.org
This article presents a stabilized nodal discontinuous Galerkin pseudospectral time-domain
(DG-PSTD) algorithm for fully anisotropic electromagnetic waves. This solver permits …

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 …

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 …

GG‐Convergence of Friedrichs Systems Revisited

K Burazin, M Erceg, M Waurick - Mathematical Methods in the …, 2025 - Wiley Online Library
We revisit the homogenization theory for Friedrichs systems. In particular, we show that GG‐
compactness can be obtained under severely weaker assumptions than in the original work …

An exact Riemann solver for wave propagation in arbitrary anisotropic elastic media with fluid coupling

Q Zhan, Q Ren, M Zhuang, Q Sun, QH Liu - Computer Methods in Applied …, 2018 - Elsevier
We present a nonconformal mesh discontinuous Galerkin pseudospectral time domain
algorithm for arbitrary anisotropic elastic/acoustic wave propagation problems. An exact …

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 …

Hybridized discontinuous Galerkin methods for wave propagation

P Fernandez, A Christophe, S Terrana… - Journal of Scientific …, 2018 - Springer
We present the recent development of hybridizable and embedded discontinuous Galerkin
(DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In …

Performance and accuracy of hybridized flux reconstruction schemes

CA Pereira, BC Vermeire - Journal of Computational Physics, 2022 - Elsevier
We present a unified framework for the hybridization of flux reconstruction (FR) schemes.
Specifically, we discuss the hybridized flux reconstruction (HFR) and interior-embedded flux …