Evidence of exponential convergence in the computation of Maxwell eigenvalues

This paper describes a finite element approach for the approximation of Maxwell eigenvalues for three-dimensional cavity problems. Hierarchical H1(Ω) and H(curl; Ω)-conforming discretisations are employed in conjunction with a technique that reduces the size of the problem to be solved. Numerical results are given on both polyhedral and curvilinear domains. These results indicate that exponential rates of convergence can be obtained with the appropriate combination of h and p-refinements.