HP-VERSION DISCONTINUOUS GALERKIN METHODS FOR HYPERBOLIC CONSERVATION-LAWS

The development of hp-version discontinuous Galerkin methods for hyper bolic conservation laws is presented in this work. A priori error esti mates are derived for a model class of linear hyperbolic conservation laws. These estimates are obtained using a new mesh-dependent norm tha t reflects the dependence of the approximate solution on the local ele ment size and the local order of approximation. The results generalize and extend previous results on mesh-dependent norms to hp-version dis continuous Galerkin methods. A posteriori error estimates which provid e bounds on the actual error are also developed in this work. Numerica l experiments verify the a priori estimates and demonstrate the effect iveness of the a posteriori estimates in providing reliable estimates of the actual error in the numerical solution.