Convergence of hp-Streamline Diffusion Method for Vlasov–Maxwell System

Journal article, 2019

In this paper we study stability and convergence for hp-streamline diffusion (SD) finite element method for the, relativistic, time-dependent Vlasov–Maxwell (VM) system. We consider spatial domain (Formula presented.) and velocities (Formula presented.) The objective is to show globally optimal a priori error bound of order (Formula presented.) for the SD approximation of the VM system; where (Formula presented.) is the mesh size and (Formula presented.) is the spectral order. Our estimates rely on the local version with hK being the diameter of the phase-space-time element K and pK the spectral order for K. The optimal hp estimates require an exact solution in the Sobolev space (Formula presented.) Numerical implementations, performed for examples in one space- and two velocity dimensions, are justifying the robustness of the theoretical results.