The streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation

We derive error estimates in the appropriate norms, for the streamline diffusion (SD) finite element methods for steady state, energy dependent, Fermi equation in three space dimensions. These estimates yield optimal convergence rates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulation is strongly consistent in the sense that the time derivative is included in the stabilization term. Here our focus is on theoretical aspects of the h and hp approximations in SD settings.