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

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...

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Bibliographic Details
Published in:Advances in computational mathematics 2016-08, Vol.42 (4), p.757-789
Main Authors: Bermúdez, A., Muñoz-Sola, R., Reales, C., Rodríguez, R., Salgado, P.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-015-9441-0