A posteriori error estimates for the one and one-half Dimensional Relativistic Vlasov–Maxwell system

Abstract

This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic VlasovMaxwell 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, or convection-dominated convection diffusion problems. The a posteriori error estimates rely on dual formulations and yield error controls based on the computable residuals. The convergence estimates are derived in negative norms, where the error is split into an iteration and an approximation error and the iteration procedure is assumed to converge.