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 …

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 …

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 and analyze an entropy-stable semi-discretization of the Euler equations based
on high-order summation-by-parts (SBP) operators. In particular, we consider general …

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 …

We are interested in the approximation of a steady hyperbolic problem. In some cases, the
solution can satisfy an additional conservation relation, at least when it is smooth. This is the …

Recently, it was discovered that the entropy-conserving/dissipative high-order split-form
discontinuous Galerkin discretizations have robustness issues when trying to solve the …

Entropy conservation and stability of numerical methods in gas dynamics have received
much interest. Entropy conservative numerical fluxes can be used as ingredients in two …

Entropy inequalities are crucial to the well-posedness of hyperbolic conservation laws,
which help to select the physically meaningful one from among the infinite many weak …

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