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Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements

Published online by Cambridge University Press:  15 April 2002

Salvatore Caorsi ,
Paolo Fernandes  and
Mirco Raffetto
Salvatore Caorsi
Affiliation:
Department of Electronics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy. (caorsi@ele.unipv.it)
Paolo Fernandes
Affiliation:
Istituto per la Matematica Applicata del Consiglio Nazionale delle Ricerche, Via De Marini 6, 16149 Genoa, Italy. (fernandes@ima.ge.cnr.it, mirco@ima.ge.cnr.it)
Mirco Raffetto
Affiliation:
Istituto per la Matematica Applicata del Consiglio Nazionale delle Ricerche, Via De Marini 6, 16149 Genoa, Italy. (fernandes@ima.ge.cnr.it, mirco@ima.ge.cnr.it)
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Abstract

By using an inductive procedure we prove that the Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec's edge element family on tetrahedral meshes are convergent and free of spurious solutions. This result is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free elements can be systematically constructed. The tools here developed are used to define a new family of spurious-free edge elements which, in some sense, are complementary to those defined in 1986 by Nedelec.

Keywords

Electromagnetic eigenproblemsnew families of edge elementsGalerkin finite element approximationsconvergencespurious modesdiscontinuous material propertiessymmetry exploitationmixed boundary conditionsdiscrete compactness.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 2 , March 2001 , pp. 331 - 354
Copyright
© EDP Sciences, SMAI, 2001

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