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Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements. (English) Zbl 0993.78016
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.

MSC:
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
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