Istituto di Matematica Applicata e Tecnologie Informatiche     
Boffi D. A note on the de Rham complex and a discrete compactness property. Preprint ercim.cnr.ian//1999-1137, 1999.
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 and show that the discrete compactness property is equivalent, in this framework, to the existence of a Fortin operator which converges in norm to the identity.
Subject Finite elements, discrete compactness, eigenvalue problems, electromagnetism
65N30, 65N25

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