Volume 47, Number 3, May-June 2013
|Page(s)||875 - 902|
|Published online||17 April 2013|
An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions∗
1 Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, 15706, Santiago de Compostela, Spain
2 Escuela de Matemáticas, Universidad Nacional de Colombia, sede Medellín, Colombia
3 CI 2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
4 Departamento de Matemática Aplicada, Escola Politécnica Superior, Universidade de Santiago de Compostela, 27002, Lugo, Spain
Received: 15 June 2012
Revised: 6 November 2012
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.
Mathematics Subject Classification: 65N30 / 78A25
Key words: Eddy current problems / time-dependent electromagnetic problems / input current intensities / voltage drops / finite elements.
The work of the authors from Universidade de Santiago de Compostela was supported by FEDER/MTM2008-02483, Ministerio de Ciencia e Innovación (Spain), and INCITE09-207047-PR and Grupos de Referencia Competitiva, Xunta de Galicia (Spain). R. Rodríguez was partially supported by BASAL project CMM, Universidad de Chile (Chile). B. López-Rodríguez was supported by MECESUP UCO0713 (Chile), Banco Santander-USC fellowship (Spain), and projects 201010010107 and 20101009545, Vicerrectoría de Investigación, Universidad Nacional de Colombia (Colombia).
© EDP Sciences, SMAI, 2013
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