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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.
@article{M2AN_2013__47_3_875_0,
author = {Berm\'udez, Alfredo and L\'opez-Rodr{\'\i}guez, Bibiana and Rodr{\'\i}guez, Rodolfo and Salgado, Pilar},
title = {An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {875--902},
publisher = {EDP-Sciences},
volume = {47},
number = {3},
year = {2013},
doi = {10.1051/m2an/2013065},
mrnumber = {3056413},
zbl = {1266.78025},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013065/}
}
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 PY - 2013 SP - 875 EP - 902 VL - 47 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013065/ DO - 10.1051/m2an/2013065 LA - en ID - M2AN_2013__47_3_875_0 ER -
%0 Journal Article %A Bermúdez, Alfredo %A López-Rodríguez, Bibiana %A Rodríguez, Rodolfo %A Salgado, Pilar %T An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 875-902 %V 47 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013065/ %R 10.1051/m2an/2013065 %G en %F M2AN_2013__47_3_875_0
Bermúdez, Alfredo; López-Rodríguez, Bibiana; Rodríguez, Rodolfo; Salgado, Pilar. 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 , Tome 47 (2013) no. 3, pp. 875-902. doi: 10.1051/m2an/2013065
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