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 …
development of the so-called hybridizable discontinuous Galerkin (HDG) methods, since …
A discrete-ordinates variational nodal method for heterogeneous neutron Boltzmann transport problems
This study introduces an unstructured variational nodal method (UVNM-S N), also
recognized as the hybridized discontinuous Galerkin (HDG) method, for solving …
recognized as the hybridized discontinuous Galerkin (HDG) method, for solving …
An adaptive high-order transient algorithm to solve large-scale anisotropic Maxwell's equations
This article presents a stabilized nodal discontinuous Galerkin pseudospectral time-domain
(DG-PSTD) algorithm for fully anisotropic electromagnetic waves. This solver permits …
(DG-PSTD) algorithm for fully anisotropic electromagnetic waves. This solver permits …
Hybridisable discontinuous Galerkin formulation of compressible flows
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 …
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 …
robust methods that can easily handle elements of arbitrary shapes, irregular triangulations …
GG‐Convergence of Friedrichs Systems Revisited
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 …
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
We present a nonconformal mesh discontinuous Galerkin pseudospectral time domain
algorithm for arbitrary anisotropic elastic/acoustic wave propagation problems. An exact …
algorithm for arbitrary anisotropic elastic/acoustic wave propagation problems. An exact …
HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB
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 …
discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of …
Hybridized discontinuous Galerkin methods for wave propagation
We present the recent development of hybridizable and embedded discontinuous Galerkin
(DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In …
(DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In …
Performance and accuracy of hybridized flux reconstruction schemes
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 …
Specifically, we discuss the hybridized flux reconstruction (HFR) and interior-embedded flux …