We propose a way of extending the discontinuous Galerkin method from pure hyperbolic equations to convection-dominated equations with an 0(h) diffusion term. The resulting method is explicit and can be applied with polynomials of degree n > 1 . The extended method satisfies the same 0(hn+ll2) error estimate previously established for the discontinuous Galerkin method as applied to hyperbolic pr...

In this paper, we develop and analyze the Runge-Kutta discontinuous Galerkin (RKDG) method to solve weakly coupled hyperbolic multi-domain problems. Such problems involve transfer type boundary conditions with discontinuous fluxes between different domains, calling for special techniques to prove stability of the RKDG methods. We prove both stability and error estimates for our RKDG methods on ...

The aim of this paper is to present and analyze a class of hpversion discontinuous Galerkin (DG) discretizations for the numerical approximation of linear elliptic problems. This class includes a number of well-known DG formulations. We will show that the methods are stable provided that the stability parameters are suitably chosen. Furthermore, on (possibly irregular) quadrilateral meshes, we ...

Article history: Received 5 October 2013 Received in revised form 19 March 2014 Accepted 20 March 2014 Available online 2 April 2014

We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in R2. In order to apply the PWDG method, we introduce an artificial boundary to truncate the domain, and we impose a non-local Dirichlet-to-Neumann (DtN) boundary conditions on the artificial curve. To define the method, we introduce ne...

We consider an exponentially fitted discontinuous Galerkin method for advection dominated problems and propose a block solver for the resulting linear systems. In the case of strong advection the solver is robust with respect to the advection direction and the number of unknowns.

In this paper, we investigate a new approach for the numerical solution of the two-dimensional depth-integrated shallow water equations, based on coupling discontinuous and continuous Galerkin methods. In this approach, we couple a discontinuous Galerkin method applied to the primitive continuity equation, coupled to a continuous Galerkin method applied to the so-called ‘‘wave continuity equati...

This work is concerned with the numerical solution of the time-harmonic Maxwell equations discretized by discontinuous Galerkin methods on unstructured meshes. Our motivation for using a discontinuous Galerkin method is the enhanced flexibility compared to the conforming edge element method [12]: for instance, dealing with non-conforming meshes is straightforward and the choice of the local app...

We prove optimal convergence rates for the approximation provided by the original discontinuous Galerkin method for the transport-reaction problem. This is achieved in any dimension on meshes related in a suitable way to the possibly variable velocity carrying out the transport. Thus, if the method uses polynomials of degree k, the L2-norm of the error is of order k+1. Moreover, we also show th...