A note on the de Rham complex and a discrete compactness property

The aim of this paper is to review the mathematical analysis of the eigenvalue problem associated with the Maxwell's system. Our analysis is quite general and can be applied to several families of edge finite element methods. Moreover, we discuss the links between different conditions that guarantee the good approximations of the eigensolutions. In particular, we prove that the commutativity of the de Rham complex implies the discrete compactness introduced by Kikuchi in [1]. (C) 2000 Elsevier Science Ltd. All rights reserved.