Accuracy of eigenvalue obtained with hybrid elements on axisymmetric domains

Eigenvalues of dipole modes in a cylindrical cavity and a spherical cavity were calculated with hybrid triangular elements assuming the sin mθ and cos mθ dependencies of the field, and compared with their analytical values. The elements are a combination of linear edge elements for r- and z-components and quadratic nodal elements for the azimuthal one. Because two out of eight degrees of freedom in the linear edge element are internal, they are often omitted. The 14-parameter elements showed a quadratic convergence on mesh refinement, while the 12-parameter ones showed the linear rate like constant edge elements