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An $ \boldsymbol{E}$-based mixed formulation for a time-dependent eddy current problem


Authors: Ramiro Acevedo, Salim Meddahi and Rodolfo Rodríguez
Journal: Math. Comp. 78 (2009), 1929-1949
MSC (2000): Primary 65N15, 65N30, 78M10
DOI: https://doi.org/10.1090/S0025-5718-09-02254-6
Published electronically: June 3, 2009
MathSciNet review: 2521273
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Abstract: In this paper, we analyze a mixed form of a time-dependent eddy current problem formulated in terms of the electric field $ \boldsymbol{E}$. We show that this formulation admits a well-posed saddle point structure when the constraints satisfied by the primary unknown in the dielectric material are handled by means of a Lagrange multiplier. We use Nédélec edge elements and standard nodal finite elements to define a semi-discrete Galerkin scheme. Furthermore, we introduce the corresponding backward-Euler fully-discrete formulation and prove error estimates.


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Additional Information

Ramiro Acevedo
Affiliation: Departamento de Matemáticas, Universidad del Cauca, Calle 5 No 4-70, Popayán, Colombia
Email: rmacevedo@unicauca.edu.co

Salim Meddahi
Affiliation: Departamento de Matemáticas, Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo, España
Email: salim@uniovi.es

Rodolfo Rodríguez
Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Email: rodolfo@ing-mat.udec.cl

DOI: https://doi.org/10.1090/S0025-5718-09-02254-6
Keywords: Eddy currents, time-dependent problems, mixed finite elements, error estimates
Received by editor(s): January 22, 2008
Received by editor(s) in revised form: November 28, 2008
Published electronically: June 3, 2009
Additional Notes: The first author was partially supported by MECESUP UCO0406 and a CONICYT Ph.D. fellowship at Universidad de Concepcion (Chile).
The second author was partially supported by the Ministerio de Educación y Ciencia of Spain, through the project No. MTM2007-65088
The third author was partially supported by FONDAP and BASAL projects, CMM, Universidad de Chile (Chile).
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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