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...

We analyze the central discontinuous Galerkin (DG) method for time-dependent linear conservation laws. In one dimension, optimal a priori L error estimates of order k+1 are obtained for the semidiscrete scheme when piecewise polynomials of degree at most k (k ≥ 0) are used on overlapping uniform meshes. We then extend the analysis to multidimensions on uniform Cartesian meshes when piecewise te...

Article history: Received 21 February 2009 Received in revised form 28 July 2009 Accepted 19 October 2009 Available online 1 November 2009