Implicit a posteriori error estimates for the Maxwell equations

An implicit a posteriori error estimation technique is presented and analyzed for the numerical solution of the time-harmonic Maxwell equations using Nédélec edge elements. For this purpose we define a weak formulation for the error on each element and provide an efficient and accurate numerical solution technique to solve the error equations locally. We investigate the well-posedness of the error equations and also consider the related eigenvalue problem for cubic elements. Numerical results for both smooth and non-smooth problems, including a problem with reentrant corners, show that an accurate prediction is obtained for the local error, and in particular the error distribution, which provides essential information to control an adaptation process. The error estimation technique is also compared with existing methods and provides significantly sharper estimates for a number of reported test cases. \u

A reliable and efficient implicit a posteriori error estimation technique for the time harmonic Maxwell equations

We analyze an implicit a posteriori error indicator for the time harmonic Maxwell equations and prove that it is both reliable and locally efficient. For the derivation, we generalize some recent results concerning explicit a posteriori error estimates. In particular, we relax the divergence free constraint for the source term. We also justify the complexity of the obtained estimator

A posteriori error estimates for streamline-diffusion and discontinuous Galerkin methods for the 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 anadd of extra diffusion to, e.g. the system of equations having hyperbolic nature, orconvection-dominated convection diffusion problems. The a posteriori error estimatesrely 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 intoan iteration and an approximation error and the iteration procedure is assumed to\ua0 converge

A Posteriori Error Analysis for the Optimal Control of Magneto-Static Fields

This paper is concerned with the analysis and numerical analysis for the optimal control of first-order magneto-static equations. Necessary and sufficient optimality conditions are established through a rigorous Hilbert space approach. Then, on the basis of the optimality system, we prove functional a posteriori error estimators for the optimal control, the optimal state, and the adjoint state. 3D numerical results illustrating the theoretical findings are presented.Comment: Keywords: Maxwell's equations, magneto statics, optimal control, a posteriori error analysi