Discrete compactness and the approximation of Maxwell's equations in R-3

We analyze the use of edge finite element methods to approximate Maxwell's equations in a bounded cavity. Using the theory of collectively compact ope rators, we prove h-convergence for the source and eigenvalue problems. This is the first proof of convergence of the eigenvalue problem for general ed ge elements, and it extends and unifies the theory for both problems. The c onvergence results are based on the discrete compactness property of edge e lement due to Kikuchi. We extend the original work of Kikuchi by proving th at edge elements of all orders possess this property.