Goal-oriented error estimation and h-adaptivity for Maxwell’s equations Original Research Article

Goal-oriented error estimates, based on dual solutions, are derived for the S-parameters of a waveguide cavity resonator and a computationally cheap method is proposed to compute these. Numerical results show that the error estimators are relatively accurate, usually well within a factor 2 from the exact errors. Adaptive mesh-refinement based on these estimates recovers optimal convergence rates for complete and incomplete, first and second order, curl-conforming finite elements of Nédélec type, despite singularities at reentrant corners. It is also shown numerically that the convergence rate is independent of the element-order when singularities are present and the mesh is refined uniformly.