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A transient eddy current problem on a moving domain. Numerical analysis

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Abstract

The aim of this paper is to introduce and analyze a numerical method to solve a transient eddy current problem which arises from the modeling of electromagnetic forming in the axisymmetric case. The resulting problem is degenerate parabolic with the time derivative acting on a moving subdomain. This paper is the sequel of Bermúdez et al. (SIAM J. Math. Anal. 45, 3629–3650, 2013), where a weak formulation of this problem was proved to be well posed and additional regularity of the solution was also established. In the present paper, we propose a finite element method in space combined with a backward Euler time scheme for its numerical solution. We obtain error estimates and report numerical results which allow us to assess the performance of the proposed method.

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Authors and Affiliations

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

    A. Bermúdez, R. Muñoz-Sola & P. Salgado

  2. Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería, Colombia

    C. Reales

  3. CI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    R. Rodríguez

Authors
  1. A. Bermúdez
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  2. R. Muñoz-Sola
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  3. C. Reales
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  4. R. Rodríguez
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  5. P. Salgado
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Corresponding author

Correspondence to C. Reales.

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Communicated by: Jan Hesthaven

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Bermúdez, A., Muñoz-Sola, R., Reales, C. et al. A transient eddy current problem on a moving domain. Numerical analysis. Adv Comput Math 42, 757–789 (2016). https://doi.org/10.1007/s10444-015-9441-0

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  • DOI: https://doi.org/10.1007/s10444-015-9441-0

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