Geodesic
Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 2, pp. 331-354

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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.

Classification : 65N25, 65N30, 65N12
Keywords: electromagnetic eigenproblems, new families of edge elements, Galerkin finite element approximations, convergence, spurious modes, discontinuous material properties, symmetry exploitation, mixed boundary conditions, discrete compactness 
@article{M2AN_2001__35_2_331_0,
     author = {Caorsi, Salvatore and Fernandes, Paolo and Raffetto, Mirco},
     title = {Spurious-free approximations of electromagnetic eigenproblems by means of {Nedelec-type} elements},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {331--354},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {2},
     year = {2001},
     mrnumber = {1825702},
     zbl = {0993.78016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_2_331_0/}
}
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Caorsi, Salvatore; Fernandes, Paolo; Raffetto, Mirco. Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 2, pp. 331-354. http://geodesic.mathdoc.fr/item/M2AN_2001__35_2_331_0/