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IMA Journal of Numerical Analysis Advance Access published online on March 12, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn063
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Numerical analysis of a finite-element method for the axisymmetric eddy current model of an induction furnace

Alfredo Bermúdez{dagger}

Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain

Carlos Reales{ddagger} and Rodolfo Rodríguez§

Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Pilar Salgado

Departamento de Matemática Aplicada, Escola Politécnica Superior, Universidade de Santiago de Compostela, 27002 Lugo, Spain

{dagger} Email: alfredo.bermudez{at}usc.es

{ddagger} Email: creales{at}ing-mat.udec.cl. Permanent address: Departamento de Matemática y Estadística, Universidad de Córdoba, Montería, Colombia

§ Corresponding author. Email: rodolfo{at}ing-mat.udec.cl

Email: mpilar.salgado{at}usc.es

Received on 4 March 2008. Revised on 8 September 2008.


  Abstract

The aim of this paper is to analyse a finite-element method to solve an eddy current problem arising from the modelling of an induction furnace. By taking advantage of the cylindrical symmetry, the three-dimensional problem reduces to a two-dimensional one on a meridional section, provided that the current density, written in cylindrical coordinates, has only an azimuthal component. A mixed formulation in appropriate weighted Sobolev spaces is given. The existence and uniqueness of the solution are proved by analysing an equivalent weak formulation. Moreover, an additional regularity result is proved under suitable assumptions on the physical coefficients. The problem is discretized by standard finite elements and a priori error estimates are proved. Finally, some numerical experiments that allow an assessment of the performance of the method are reported.

Key Words: low-frequency harmonic Maxwell equations; eddy current problems; finite-element computational electromagnetism; axisymmetric problems


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