Classical nite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element, on domains which physical boundaries are indi erently straight or curved. This approximation represents serious hindrance for high-order methods, since they limit the precision of the spatial discretization to second order. Thus, exploiting an enhanced representatio...

The local discontinuous Galerkin (LDG) viscous flux formulation was originally developed by Cockburn and Shu for the discontinuous Galerkin setting and later extended to the spectral volume setting by Wang and his collaborators. Unlike the penalty formulations like the interior penalty and the BR2 schemes, the LDG formulation requires no length based penalizing terms and is compact. However, co...

We analyze the classical discontinuous Galerkin method for a general parabolic equation. Symmetric error estimates for schemes of arbitrary order are presented. The ideas we develop allow us to relax many assumptions freqently required in previous work. For example, we allow different discrete spaces to be used at each time step and do not require the spatial operator to be self adjoint or inde...

We report on recent efforts towards the development of a high order, non-conforming, discontinuous Galerkin method for the solution of the system of frequency domain Maxwell’s equations in heterogeneous propagation media. This method is an extension of the low order one which was proposed in [1].

In this paper we provide estimates to the rate of convergence of the nonlinear Galerkin approximation method. In particular, and by means of an illustrative example, we show that the nonlinear Galerkin method converges faster than the usual Galerkin method.

1 Tankers moored at an oil production center.

The discontinuous Galerkin (DG) scheme is used to solve a conserved higher-order (CHO) traffic flow model by exploring several Riemann solvers. The second-order accurate DG scheme is found to be adequate in that the accuracy is comparable to the weighted essentially non-oscillatory (WENO) scheme with fifth-order accuracy and much better than the scheme with first-order accuracy in resolving a w...

A Comparison between the Discontinuous Galerkin Method and the High Resolution Wave Propagation Algorithm for the Full Two-Fluid Plasma Model

89 Acknowledgements 91