An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions

Alfredo Bermúdez; Bibiana López-Rodríguez; Rodolfo Rodríguez; Pilar Salgado

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 3, page 875-902
  • ISSN: 0764-583X

Abstract

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The aim of this paper is to analyze a formulation of the eddy current problem in terms of a time-primitive of the electric field in a bounded domain with input current intensities or voltage drops as source data. To this end, we introduce a Lagrange multiplier to impose the divergence-free condition in the dielectric domain. Thus, we obtain a time-dependent weak mixed formulation leading to a degenerate parabolic problem which we prove is well-posed. We propose a finite element method for space discretization based on Nédélec edge elements for the main variable and standard finite elements for the Lagrange multiplier, for which we obtain error estimates. Then, we introduce a backward Euler scheme for time discretization and prove error estimates for the fully discrete problem, too. Finally, the method is applied to solve a couple of test problems.

How to cite

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Bermúdez, Alfredo, et al. "An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.3 (2013): 875-902. <http://eudml.org/doc/273097>.

@article{Bermúdez2013,
abstract = {The aim of this paper is to analyze a formulation of the eddy current problem in terms of a time-primitive of the electric field in a bounded domain with input current intensities or voltage drops as source data. To this end, we introduce a Lagrange multiplier to impose the divergence-free condition in the dielectric domain. Thus, we obtain a time-dependent weak mixed formulation leading to a degenerate parabolic problem which we prove is well-posed. We propose a finite element method for space discretization based on Nédélec edge elements for the main variable and standard finite elements for the Lagrange multiplier, for which we obtain error estimates. Then, we introduce a backward Euler scheme for time discretization and prove error estimates for the fully discrete problem, too. Finally, the method is applied to solve a couple of test problems.},
author = {Bermúdez, Alfredo, López-Rodríguez, Bibiana, Rodríguez, Rodolfo, Salgado, Pilar},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Eddy current problems; time-dependent electromagnetic problems; input current intensities; voltage drops; finite elements; eddy current problems},
language = {eng},
number = {3},
pages = {875-902},
publisher = {EDP-Sciences},
title = {An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions},
url = {http://eudml.org/doc/273097},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Bermúdez, Alfredo
AU - López-Rodríguez, Bibiana
AU - Rodríguez, Rodolfo
AU - Salgado, Pilar
TI - An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 3
SP - 875
EP - 902
AB - The aim of this paper is to analyze a formulation of the eddy current problem in terms of a time-primitive of the electric field in a bounded domain with input current intensities or voltage drops as source data. To this end, we introduce a Lagrange multiplier to impose the divergence-free condition in the dielectric domain. Thus, we obtain a time-dependent weak mixed formulation leading to a degenerate parabolic problem which we prove is well-posed. We propose a finite element method for space discretization based on Nédélec edge elements for the main variable and standard finite elements for the Lagrange multiplier, for which we obtain error estimates. Then, we introduce a backward Euler scheme for time discretization and prove error estimates for the fully discrete problem, too. Finally, the method is applied to solve a couple of test problems.
LA - eng
KW - Eddy current problems; time-dependent electromagnetic problems; input current intensities; voltage drops; finite elements; eddy current problems
UR - http://eudml.org/doc/273097
ER -

References

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