On a Canonical form for Maxwell Equations and Convergence of Finite Element Scheme for Vlasov--Maxwell system.

This work is a swift introduction to the nature of governing laws involved in the Maxwell equations. We then approximate a “one and one-half” dimensional relativistic Vlasov-Maxwell (VM) system using streamline diffusion finite element method. In this geometry d’Alembert representation for the fields functions guarantees the existence of a unique solution of the Maxwell equations. The VM system is then approximated using the streamline diffusion finite element method. In this part we derive some stability inequalities and optimal a priori error estimates due to the maximal available regularity of the exact solution