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

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 …

An overview of the software design and data abstraction decisions chosen for deal. II, a
general purpose finite element library written in C++, is given. The library uses advanced …

We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes
having test function spaces that are automatically computable to guarantee stability. Given a …

This monograph is the first to provide a comprehensive, self-contained and rigorous
presentation of some of the most powerful preconditioning methods for solving finite element …

A new space–time discontinuous Galerkin finite element method for the solution of the Euler
equations of gas dynamics in time-dependent flow domains is presented. The discontinuous …

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 …