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

Salvatore Caorsi; Paolo Fernandes; Mirco Raffetto

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 2, page 331-354
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Caorsi, Salvatore, Fernandes, Paolo, and Raffetto, Mirco. "Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements." ESAIM: Mathematical Modelling and Numerical Analysis 35.2 (2010): 331-354. <http://eudml.org/doc/197426>.

@article{Caorsi2010,
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. },
author = {Caorsi, Salvatore, Fernandes, Paolo, Raffetto, Mirco},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
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.; electromagnetic eigenproblems; new families of edge elements; convergence; symmetry exploitation; discrete compactness},
language = {eng},
month = {3},
number = {2},
pages = {331-354},
publisher = {EDP Sciences},
title = {Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements},
url = {http://eudml.org/doc/197426},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Caorsi, Salvatore
AU - Fernandes, Paolo
AU - Raffetto, Mirco
TI - Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 2
SP - 331
EP - 354
AB - 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.
LA - eng
KW - Electromagnetic eigenproblems; new families of edge elements; Galerkin finite element approximations; convergence; spurious modes; discontinuous material properties; symmetry exploitation; mixed boundary conditions; discrete compactness.; electromagnetic eigenproblems; new families of edge elements; convergence; symmetry exploitation; discrete compactness
UR - http://eudml.org/doc/197426
ER -

References

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