A coupled steady thermo-electromagnetic problem in axisymmetric geometries. Mathematical and numerical analysis

  1. Gómez, Dolores 12
  2. López-Rodríguez, Bibiana 3
  3. Salgado, Pilar 12
  4. Venegas, Pablo 45
  1. 1 Departamento de Matemática Aplicada, Universidade de Santiago de Compostela , E-15782 Santiago de Compostela, Spain
  2. 2 CITMAga, Galician Centre for Mathematical Research and Technology , E-15782 Santiago de Compostela, Spain
  3. 3 Departamento de Matemáticas, Universidad Nacional de Colombia , sede Medellín, Colombia
  4. 4 GIMNAP , Departamento de Matemática, , Concepción 4051381, Chile
  5. 5 Universidad del Bío-Bío , Departamento de Matemática, , Concepción 4051381, Chile
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Journal:
IMA Journal of Numerical Analysis

ISSN: 0272-4979,  1464-3642

Year of publication: 2024

Type: Article

DOI: 10.1093/IMANUM/DRAE056 WoS: WOS:001314137100001 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: IMA Journal of Numerical Analysis

Abstract

This paper focuses on the analysis of a steady thermo-electromagnetic problem related to the modeling of induction heating processes. Taking advantage of the cylindrical symmetry, the original three-dimensional problem can be reduced to a two-dimensional one on a meridional section, provided that the current density has only the azimuthal component. A variational formulation is presented in appropriately weighted Sobolev spaces, and the existence of a solution is established by employing a fixed-point argument. Furthermore, uniqueness and additional regularity results are proved under reasonable assumptions on the physical coefficients. A finite element approximation combined with a fixed-point iteration scheme is proposed for the numerical solution of the problem. A priori error estimates are obtained to quantify the accuracy of the approximation. Finally, numerical results are reported to validate the theoretical estimates and assess the performance of the method in a physical application.

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