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 …

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 the present paper we develop a new family of Virtual Elements for the Stokes problem on
polygonal meshes. By a proper choice of the Virtual space of velocities and the associated …

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

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 …

We present an implicit high-order hybridizable discontinuous Galerkin method for the steady-
state and time-dependent incompressible Navier–Stokes equations. The method is devised …

This paper is a short essay on discontinuous Galerkin methods intended for a very wide
audience. We present the discontinuous Galerkin methods and describe and discuss their …

In this paper a new local discontinuous Galerkin method for the incompressible stationary
Navier-Stokes equations is proposed and analyzed. Four important features render this …

In this paper, we review the development of the so-called local discontinuous Galerkin
method for linearized incompressible fluid flow. This is a stable, high-order accurate and …

We present a class of discontinuous Galerkin methods for the incompressible Navier–Stokes
equations yielding exactly divergence-free solutions. Exact incompressibility is achieved by …