In this paper we will review a recent emerging paradigm shift in the construction and
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …

As computational astrophysics comes under pressure to become a precision science, there
is an increasing need to move to high accuracy schemes for computational astrophysics …

The framework of inner product norm preserving relaxation Runge--Kutta methods [DI
Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850--2870] is extended to general convex …

The paper presents two contributions in the context of the numerical simulation of
magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics …

The book covers intimately all the topics necessary for the development of a robust
magnetohydrodynamic (MHD) code within the framework of the cell-centered finite volume …

The first paper of this series presents a discretely entropy stable discontinuous Galerkin
(DG) method for the resistive magnetohydrodynamics (MHD) equations on three …

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

We develop an entropy–stable two–phase incompressible Navier–Stokes/Cahn–Hilliard
discontinuous Galerkin (DG) flow solver method. The model poses the Cahn–Hilliard …

We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for
ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi …

We describe a unique averaging procedure to design an entropy stable dissipation operator
for the ideal magnetohydrodynamic (MHD) and compressible Euler equations. Often in the …