TOWARDS A GOOD CHARACTERIZATION OF SPECTRALLY CORRECT FINITE-ELEMENT METHODS IN ELECTROMAGNETICS

Spurious modes often appear in the computed spectrum when an electroma gnetic eigenproblem is solved by the finite element method. Demonstrat es that the inclusion condition, often claimed as the theoretical reas on for the absence of (non-zero frequency) spurious modes, is a suffic ient but not necessary condition for that. Does this by proving that e dge elements, which are spectrally correct, do not satisfy the inclusi on condition. As intermediate steps towards this result, proves the eq uivalence of the inclusion condition to a less cryptic one and gives t wo more easily-checked necessary conditions for the latter. Concludes that from this investigation, the inclusion condition seems too strong to be useful as a sufficient condition. Works out the present analysi s in the framework of spectral approximation theory for non-compact op erators, which emerges as a basic tool for a deeper understanding of t he whole question of spurious modes.