A posteriori error estimates for the one and one-half Dimensional   Relativistic Vlasov-Maxwell system
  This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic Vlasov-Maxwell system. The SD scheme yields a weak formulation, that corresponds to an add of extra diffusion to, e.g. the system of equations having hyperbolic nature, and convection-dominated convection diffusion problems. A procedure that improves the convergence of finite elements for this type of problems. The a posteriori error estimates relay on a dual problem formulation and yields an error control based on the, computable, residual of the approximate solution. The lack of dissipativity enforces us considering negative norm estimates. To derive these estimates, the error term is split into an iteration and an approximation error where the iteration procedure is assumed to converge. The computational aspects and implementations, which justify the theoretical results of this part, are the subject of these studies and addressed in [5]. 
Mohammad Asadzadeh and Christoffer Standar
math.NA