Hp-dgfem for Partial Diierential Equations with Nonnegative Characteristic Form

We develop the error analysis for the hp-version of a discontinuous nite element approximation to second-order partial diierential equations with non-negative characteristic form. This class of equations includes classical examples of second-order elliptic and parabolic equations, rst-order hyperbolic equations , as well as equations of mixed type. We establish an a priori error bound for the method which is of optimal order in the mesh size h and 1 order less than optimal in the polynomial degree p. In the particular case of a rst-order hyperbolic equation the error bound is optimal in h and 1=2 an order less than optimal in p.