Weak Formulations for Finite Element Analysis of an Electromagnetic Eigenvalue Problem

This paper presents some weak (or variational) formulations for an electromagnetic eigenvalue problem related to the analysis of cavity resonators in microwave theory. Particularly, mixed and penalty formulations are considered, since they appear to be applicable to finite element analysis of such a problem. Moreover, some theoretical results are derived for these formulations. Then, a simple two-dimensional finite element is developed by the penalty formulation, and tested by numerical computations. We point out some numerical difficulties observed in this type of piecewise polynomial finite elements based on the penalty approach