Estimating errors in design sensitivities

Design sensitivities are useful quantities that may be efficiently computed by finite element analysis, from the field solution and its adjoint. However, the computed sensitivities are subject to discretization error. A method is described for the a posteriori estimation of this error, making use of the properties of hierarchal finite elements. The method is applied to the sensitivities of microwave scattering parameters, computed with three-dimensional tetrahedral elements. Results for a waveguide filter, a waveguide transformer, and a magic T demonstrate the quality of the estimator.