In this paper, we review the development of the Runge–Kutta discontinuous Galerkin
(RKDG) methods for non-linear convection-dominated problems. These robust and accurate …

We provide a framework for the analysis of a large class of discontinuous methods for
second-order elliptic problems. It allows for the understanding and comparison of most of the …

In this paper, we present an overview of the evolution of the discontinuous Galerldn methods
since their introduction in 1973 by Reed and Hill, in the framework of neutron transport, until …

In this paper, we present the first a priori error analysis for the local discontinuous Galerkin
(LDG) method for a model elliptic problem. For arbitrary meshes with hanging nodes and …

In this paper, we present a superconvergence result for the local discontinuous Galerkin
(LDG) method for a model elliptic problem on Cartesian grids. We identify a special …

In this paper, we introduce and analyze local discontinuous Galerkin methods for the Stokes
system. For a class of shape regular meshes with hanging nodes we derive a priori …

We study the convergence properties of the $ hp $-version of the local discontinuous
Galerkin finite element method for convection-diffusion problems; we consider a model …

We provide a common framework for the understanding, comparison, and analysis of
several discontinuous Galerkin methods that have been proposed for the numerical …

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG)
framework is developed for fluid interface dynamics, facilitating precise computation of …

This paper presents a review of the so-called Local Discontinuous Galerkin (LDG) method
applied to elliptic problems. The method is presented using a mixed formulation similar to …