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 study the local discontinuous Galerkin (LDG) methods for nonlinear, time-
dependent convection-diffusion systems. These methods are an extension of the Runge …

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

This work is devoted to the theory and approximation of nonlinear hyper bolic systems of
conservation laws in one or two space variables. It follows directly a previous publication on …

During recent years the authors and collaborators have been involved in an activity related
to the construction and analysis of large time step operator splitting algorithms for the …

This paper summarises the results of a benchmark study that compares a number of
mathematical and numerical models applied to specific problems in the context of carbon …

This paper presents a new method which exhibits the best features of both finite volume and
finite element techniques. Special attention is given to the issues of conservation, flexible …

We present an extension of the discontinuous Galerkin method which is applicable to the
numerical solution of diffusion problems. The method involves a weak imposition of …

The book has grown out of a concerted research effort over the last decade. We have
enjoyed collaboration with many good friends and colleagues on these problems, in …

This paper presents a unified analysis of discontinuous Galerkin methods to approximate
Friedrichs' systems. An abstract set of conditions is identified at the continuous level to …