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. © The Author(s) 2024. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.