A posteriori error estimates for streamline-diffusion and discontinuous Galerkin methods for the Vlasov-Maxwell system

Journal article, 2018

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, 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.