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

Published online by Cambridge University Press:  17 April 2013

Alfredo Bermúdez ,
Bibiana López-Rodríguez ,
Rodolfo Rodríguez  and
Pilar Salgado
Alfredo Bermúdez
Affiliation:
Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, 15706, Santiago de Compostela, Spain. alfredo.bermudez@usc.es
Bibiana López-Rodríguez
Affiliation:
Escuela de Matemáticas, Universidad Nacional de Colombia, sede Medellín, Colombia; blopezr@unal.edu.co
Rodolfo Rodríguez
Affiliation:
CI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile; rodolfo@ing-mat.udec.cl
Pilar Salgado
Affiliation:
Departamento de Matemática Aplicada, Escola Politécnica Superior, Universidade de Santiago de Compostela, 27002, Lugo, Spain; mpilar.salgado@usc.es
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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.

Keywords

Eddy current problemstime-dependent electromagnetic problemsinput current intensitiesvoltage dropsfinite elements.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 3 , May 2013 , pp. 875 - 902
Copyright
© EDP Sciences, SMAI, 2013

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