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 …

High order methods based on diagonal-norm summation by parts operators can be shown
to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of …

In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin
(ADER-DG) method. To obtain this desired result, we equip the space part of the method …

The construction of high order entropy stable collocation schemes on quadrilateral and
hexahedral elements has relied on the use of Gauss--Legendre--Lobatto collocation points …

This work examines the development of an entropy conservative (for smooth solutions) or
entropy stable (for discontinuous solutions) space–time discontinuous Galerkin (DG) method …

In this paper, we will build a roadmap for the growing literature of high order quadrature-
based entropy stable discontinuous Galerkin (DG) methods, trying to elucidate the …

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for
hyperbolic conservation laws that satisfy invariant domain preserving properties using …

This work reports on the performances of a fully-discrete hp-adaptive entropy stable
discontinuous collocated Galerkin method for the compressible Naiver–Stokes equations …

High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and
Navier-Stokes equations require the positivity of thermodynamic quantities in order to …

Many modern discontinuous Galerkin (DG) methods for conservation laws make use of
summation by parts operators and flux differencing to achieve kinetic energy preservation or …