This article reviews several unstructured grid-based high-order methods for the
compressible Euler and Navier–Stokes equations. We treat the spatial and temporal …

In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an
attractive approach for numerical simulations of compressible flows. This paper presents an …

Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

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 …

Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element
discretization to resolve a shock layer within a single cell. However, when a non-smooth …

We study preconditioners for the iterative solution of the linear systems arising in the implicit
time integration of the compressible Navier–Stokes equations. The spatial discretization is …

We present hybridizable discontinuous Galerkin methods for solving steady and time-
dependent partial differential equations (PDEs) in continuum mechanics. The essential …

A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution
of the compressible Navier–Stokes equations on arbitrary grids. The RDG method, originally …

This article presents matrix-free finite-element techniques for efficiently solving partial
differential equations on modern many-core processors, such as graphics cards. We …

The goal of this paper is to investigate and develop a fast and robust algorithm for the
solution of high-order accurate discontinuous Galerkin discretizations of non-linear systems …