On Convergence of the Streamline Diffusion and Discontinuous Galerkin Methods for the Multi-Dimensional Fermi Pencil Beam Equation

Abstract

We derive error estimates in the $L_2$ norms, for the streamline diffusion (SD) and discontinuous Galerkin (DG) 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. Here our focus is on theoretical aspects of the $h$ and $hp$ approximations in both SD and DG settings.