Convergence of hp streamline diffusion method for Vlasov-Maxwell System

We study stability and convergence of hp-streamline diffusion (SD) finite element method for therelativistic Vlasov-Maxwell (VM) system. We consider full spatial domain in R3 and velocities in R3 . The objective is to show globally optimal a priori error bounds of order O(h/p)s+1/2 .Here h is the mesh size and p is spectral order. Our estimates rely on thelocal version where hK is the diameter of the phase-space-time element K and pK the spectral order