Finite elements with divergence-free shape function and the application to inhomogeneously-loaded waveguide analysis

A simple mixed triangular edge element is proposed for the finite elements, with which inhomogeneously-loaded and arbitrarily shaped waveguides are analyzed. The shape functions used for approximating the fields are found analytically to be divergence-free. The formulation has been found to encounter spurious-free solutions. As evidence, the non-physical solutions that appeared in the longitudinal component finite element formulation are shown to be absent in the present formulation. A comparison with another mixed element is furnished here in order to demonstrate the advantages provided by the present element.