hp-Version discontinuous Galerkin methods for hyperbolic conservation laws

Thc devclopment of hp·version discontinuous Galerkin methods for hyperholic conservalion laws is presented in this work. A priori error estimates are dcrived for a model class of linear hyperbolic conservation laws. These estimates arc obtained using a ncw mesh-dependcnt norm that rel1ects thc dependcnce of the approximate solution on thc local element size and the local order of approximation. The results generalize and extend previous results on mesh-dependent norms to hp-version discontinuous Galerkin IIlcthods. A posteriori error estimates which provide hounds on Ihe actual error ,lrC also developed in this work. Numerical experiments verify the a priori estimates and demonstrate the effectiveness of the a postcriori estimates in providing reliable estimates of the actual error in the numerical solution.