Estimating and correcting errors in scattering parameters of multiport waveguide structures computed by the finite-element method

Scattering parameters computed by the finite-element method (FEM) are necessarily subject to discretisation error. It has been shown how this error can be estimated by a quite inexpensive postprocessing operation. An estimate of the error in the field is first obtained by increasing the polynomial order of all the elements and solving the resulting system approximately. Then a carefully chosen linear functional is applied to obtain the error in the scattering parameter from the error in the field. In the paper, the method is extended to obtain estimates over a frequency band, thus providing information about the frequency error of key points, such as transmission peaks or nulls. Moreover, it is shown that the error estimates can be used to correct the computed solution, offering significant improvements in accuracy. Numerical results are obtained with hierarchal, tetrahedral finite elements, applied to an E-plane T-junction, a metallic post in a waveguide, and a waveguide bend.