We present artificial boundary conditions for the numerical simulation of nonlinear Euler equations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis which follows the Euler equations and are applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the pr...

Discontinuous Galerkin (DG) finite-element methods for secondand fourth-order elliptic problems were introduced about three decades ago. These methods stem from the hybrid methods developed by Pian and his coworker [25]. At the time of their introduction, DG methods were generally called interior penalty methods, and were considered by Baker [4], Douglas Jr. [14], and Douglas Jr. and Dupont [15...

In this paper we consider discontinuous Galerkin (DG) finite element approximations of a model scalar linear hyperbolic equation. We show that in order to ensure continuous stabilization of the method it suffices to add a jump-penalty-term to the discretized equation. In particular, the method does not require upwinding in the usual sense. For a specific value of the penalty parameter we recove...

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approxima...

This artic!e considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. _Veighted residual approxim...

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary value problems in three dimensional polyhedral domains. In order to resolve possible corner-, edgeand corneredge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined towards the corresponding ne...

Preconditioning of Discontinuous Galerkin Methods for Second Order Elliptic Problems. (December 2007) Veselin Asenov Dobrev, B.S., Sofia University Chair of Advisory Committee: Dr. Raytcho Lazarov We consider algorithms for preconditioning of two discontinuous Galerkin (DG) methods for second order elliptic problems, namely the symmetric interior penalty (SIPG) method and the method of Baumann ...

We consider Maxwell’s equations with impedance boundary conditions on a polyhedron with polyhedral holes. Well-posedness of the variational formulation is proven and a discontinuous Galerkin (dG) approximation is introduced. We prove well-posedness of the dG problem as well as a priori error estimates. Next, we use the frequency ω as a parameter in a multi-query context. For this purpose, we de...

In this paper we introduce and analyze some non-overlapping multiplicative Schwarz methods for discontinuous Galerkin (DG) approximations of elliptic problems. The construction of the Schwarz preconditioners is presented in a unified framework for a wide class of DG methods. For symmetric DG approximations we provide optimal convergence bounds for the corresponding error propagation operator, a...

SUMMARY In this work we propose and analyse a discontinuous Galerkin (DG) method for the Stokes problem based on an artificial compressibility numerical flux. A crucial step in the definition of a DG method is the choice of the numerical fluxes, which affect both the accuracy and the order of convergence of the method. We propose here to treat the viscous and the inviscid terms separately. The ...