Bermúdez de Castro López-Varela, AlfredoLópez-Rodríguez, BibianaPena, Francisco JoséRodríguez, RodolfoSalgado Rodríguez, María del PilarVenegas, Pablo2024-02-062024-02-062022Bermúdez, López-Rodríguez, Pena, Rodríguez, Salgado, & Venegas. (2022). Numerical Solution of an Axisymmetric Eddy Current Model with Current and Voltage Excitations. Journal of Scientific Computing, 91(1). https://doi.org/10.1007/S10915-022-01780-40885-7474http://hdl.handle.net/10347/32400This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10915-022-01780-4The aim of this paper is to study the numerical approximation of an axisymmetric time-harmonic eddy current problem involving an in-plane current. The analysis of the problem restricts to the conductor. The source of the problem is given in terms of boundary data currents and/or voltage drops defined in the so-called electric ports, which are parts of the boundary connected to exterior sources. This leads to an elliptic problem written in terms of the magnetic field with nonlocal boundary conditions. First, we prove the existence and uniqueness of the solution for a weak formulation written in terms of Sobolev spaces with appropriate weights. We show that the magnetic field is not the most appropriate variable to impose the boundary conditions when Lagrangian finite elements are used to discretize the problem. We propose an alternative weak formulation of the problem which allows us to avoid this drawback. We compute the numerical solution of the problem by using Lagrangian finite elements ad hoc modified on the vicinity of the symmetry axis. We provide a convergence result under rather general conditions. Moreover, we prove quasi-optimal order error estimates under additional regularity assumptions. Finally, we report numerical results which allow us to confirm the theoretical estimates and to assess the performance of the proposed method in a physical application which is the motivation of this paper: the computation of the current density distribution in a steel cylindrical bar submitted to electric-upsetting.engCopyright © 2022, The Author(s), under exclusive licence to Springer Science Business Media, LLC, part of Springer Naturehttp://creativecommons.org/licenses/by-nc-nd/4.0/Axisymmetric problemEddy-current modelFinite elementsError estimatesjournal article10.1007/s10915-022-01780-41573-7691open access