Goal-oriented error-estimation for S-parameter computations

Accurate and efficient goal-oriented error estimates for adaptive finite-element computations of scattering parameters are presented. The estimates are derived using dual problems and computed using special hierarchical basis functions, tailored to agree with the Ne´de´lec interpolant. The method is tested on a two-dimensional waveguide cavity resonator with several reentrant corners. When uniform mesh refinement is used, the convergence rate is limited to h⁴3/, independently of the element order due to singularities. However, with adaptive h-refinement guided by the presented error estimates, the convergence rate is increased to h^2p for elements of (complete or incomplete) order p≤3, even in the presence of singularities. Further, the accuracy of the scattering parameters can be increased significantly by adding the estimated errors to the computed results.