This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

In this work we show that the flexibility of the discontinuous Galerkin (dG) discretization can
be fruitfully exploited to implement numerical solution strategies based on the use of …

In this work we consider a special implementation of a discontinuous Galerkin (DG) method
for general unstructured hexahedral element meshes called the discontinuous Galerkin …

The newly developed unifying discontinuous formulation named the correction procedure
via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes …

We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic
wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal …

A family of weak Galerkin finite element discretizations is developed for solving the coupled
Darcy–Stokes equation. The equation in consideration admits the Beaver–Joseph–Saffman …

The purpose of this paper is to assess the accuracy of a discontinuous Galerkin (DG)
method for the direct numerical simulation (DNS) of freely decaying and wall-bounded …

In this paper, the ability of high-order flux reconstruction numerical schemes to perform
accurate and stable computations of compressible turbulent flows on coarse meshes is …

We consider a family of explicit one-step time discretizations for finite volume and
discontinuous Galerkin schemes, which is based on a predictor-corrector formulation. The …

We propose a new high order accurate nodal discontinuous Galerkin (DG) method for the
solution of nonlinear hyperbolic systems of partial differential equations (PDE) on …