Stabilized hp-finite element methods for first-order hyperbolic problems

We analyze the hp-version of the streamline-diffusion finite element method (SDFEM) and of the discontinuous Galerkin finite element method (DGFEM) fo r first-order linear hyperbolic problems. For both methods, we derive new e rror estimates on general finite element meshes which are sharp in the mesh -width h and in the spectral order p of the method, assuming that the stabi lization parameter is O(h/p). For piecewise analytic solutions, exponential convergence is established on quadrilateral meshes. For the DGFEM we admit very general irregular meshes and for the SDFEM we allow meshes which cont ain hanging nodes. Numerical experiments confirm the theoretical results.