Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements
Electronics, University of Pavia, Via Ferrata 1, 27100
Pavia, Italy. (firstname.lastname@example.org)
2 Istituto per la Matematica Applicata del Consiglio Nazionale delle Ricerche, Via De Marini 6, 16149 Genoa, Italy. (email@example.com, firstname.lastname@example.org)
Revised: 29 January 2001
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.
Mathematics Subject Classification: 65N25 / 65N30 / 65N12
Key words: Electromagnetic eigenproblems / new families of edge elements / Galerkin finite element approximations / convergence / spurious modes / discontinuous material properties / symmetry exploitation / mixed boundary conditions / discrete compactness.
© EDP Sciences, SMAI, 2001