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 …

In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an
attractive approach for numerical simulations of compressible flows. This paper presents an …

We present a general family of subcell limiting strategies to construct robust high-order
accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct …

This paper presents an overview of the functionalities and applications of Exasim, an open-
source code for generating high-order discontinuous Galerkin codes to numerically solve …

The second paper of this series presents two robust entropy stable shock-capturing methods
for discontinuous Galerkin spectral element (DGSEM) discretizations of the compressible …

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 …

High-order methods are being recognized as powerful tools for handling scale-resolving
simulations over complex geometry. However, several obstacles still block their complete …

In this paper, we show that diagonal-norm summation by parts (SBP) discretizations of
general non-conservative systems of hyperbolic balance laws can be rewritten as a finite …

High-order discontinuous Galerkin (DG) methods have emerged as an attractive approach
for large eddy simulation of turbulent flows owing to their high accuracy and implicit …

We introduce a new hybridized discontinuous Galerkin method for the incompressible
magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and …