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 …

This work presents an entropy stable discontinuous Galerkin (DG) spectral element
approximation for systems of non-linear conservation laws with general geometric (h) and …

We present the latest developments of our High-Order Spectral Element Solver (Image 1),
an open source high-order discontinuous Galerkin framework, capable of solving a variety of …

The main result in this paper is a provably entropy stable shock capturing approach for the
high order entropy stable Discontinuous Galerkin Spectral Element Method (DGSEM) based …

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 …

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 …

Many real-world problems involve fluids in motion. The goal of this book is to propose a new
approach to numerical analysis of the underlying nonlinear equations in the spirit of the …

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 …

Recently, element based high order methods such as Discontinuous Galerkin (DG) methods
and the closely related flux reconstruction (FR) schemes have become popular for …

A theoretical analysis of the entropy conservation properties is conducted to explain the
different behaviors of the non-dissipative finite-difference spatial discretization schemes …