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 …

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 …

For the general class of residual distribution (RD) schemes, including many finite element
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …

Recently, an approach known as relaxation has been developed for preserving the correct
evolution of a functional in the numerical solution of initial-value problems, using Runge …

In computational fluid dynamics, the demand for increasingly multidisciplinary reliable
simulations, for both analysis and design optimization purposes, requires transformational …

Recently, relaxation methods have been developed to guarantee the preservation of a
single global functional of the solution of an ordinary differential equation. Here, we …

We present a novel technique for the imposition of non-linear entropy conservative and
entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations …

We propose a new paradigm for designing efficient p-adaptive arbitrary high-order methods.
We consider arbitrary high-order iterative schemes that gain one order of accuracy at each …

We construct entropy conservative and entropy stable discontinuous Galerkin (DG)
discretizations for time-dependent nonlinear hyperbolic conservation laws on curvilinear …

Methodologies are presented that enable the construction of provably linearly stable and
conservative high-order discretizations of partial differential equations in curvilinear …