Stabilised hp-finite element approximation of partial differential equations with nonnegative characteristic form

This paper is devoted to the a priori error analysis of the hp-version of a streamline-diffusion finite element method For partial differential equati ons with nonnegative characteristic Term. This class of equations includes second-order elliptic and parabolic problems, first-order hyperbolic proble ms and second-order problems of mixed elliptic-parabolic-hyperbolic type. W e derive error bounds which are simultaneously optimal in both the mesh siz e h and the spectral order p. Numerical examples are presented to confirm t he theoretical results.