Ks. Bey et Jt. Oden, HP-VERSION DISCONTINUOUS GALERKIN METHODS FOR HYPERBOLIC CONSERVATION-LAWS, Computer methods in applied mechanics and engineering, 133(3-4), 1996, pp. 259-286
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.