Maxwell eigenvalues and discrete compactness in two dimensions

We present an elementary proof of the discrete compactness result for a gen eral class of hp finite elements introduced in [1,2]. We discuss h-converge nce of 2D elements only, and in this context, the results are not new as th e analysis of H(curl)-conforming elements for Maxwell's equations can be re duced to the long-known results for Raviart-Thomas elements [3]. The work i s based on the result of Kikuchi [4,5] for Nedelec's edge triangular elemen ts of the lowest order and presents an alternative to techniques presented in [3,6]. In particular, the present version does not use an inverse inequa lity argument, and therefore, is valid for h-adaptive meshes. We conclude t he presentation with a number of 2D computational experiments, including no nconvex domains. (C) 2000 Elsevier Science Ltd. All rights reserved.