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 …

In the present paper, a brief survey on computational techniques for the different classes of
singularly perturbed problems is given. This survey is a continuation of work performed …

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 …

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 …

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

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

This book is an introduction to a family of discontinuous Galerkin (DG) methods applied to
some steady-state and time-dependent model problems. A special effort was made to have …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

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 develop a local discontinuous Galerkin method for solving KdV type
equations containing third derivative terms in one and two space dimensions. The method is …