Discretization of the convection term in a three-cell compact stencil has been widely used in
Computational Fluid Dynamics (CFD) of engineering because the second-order …

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 …

Abstract Fisher and Carpenter (2013)[12] found a remarkable equivalence of general
diagonal norm high-order summation-by-parts operators to a subcell based high-order finite …

It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy
cell entropy inequalities for the square entropy for both scalar conservation laws (Jiang 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 …

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 …

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 construct a local Lax–Friedrichs type positivity-preserving flux for compressible Navier–
Stokes equations, which can be easily extended to multiple dimensions for generic forms 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 …