An evaluation of mixed-order versus full-order vector finite elements

Recently proposed vector finite elements are compared to previously published elements, and independently implemented and validated in the context of rectangular waveguide analysis. Both mixed-order and full-order elements up to order two are considered. The use of quadrature (cubature) to evaluate the finite element system matrices is discussed. Details of some analytical work required before quadrature is applied are presented for several types of basis functions. For many RF applications, mixed-order elements offer optimal accuracy for a given number of degrees of freedom, and an empty ("through") waveguide solution verifies this, with similar convergence rates for mixed- and full-order elements of the same order. However, a capacitive iris in the rectangular waveguide, with a solution dominated by the quasi-static electric field, motivates the use of full-order elements in such cases. Results for the electric fields in the vicinity of the iris also demonstrate the enhanced accuracy of the full-order elements here. This is further illustrated using a dielectric load in a waveguide, where complete order elements produce a better approximation of the normal jump discontinuity. Although this paper addresses guided wave problems, the results are also applicable to radiation and scattering problems.