Acevedo, RamiroGómez, ChristianLópez-Rodríguez, BibianaSalgado Rodríguez, María del Pilar2024-02-062024-02-062023Acevedo, R., Gómez, C., López-Rodríguez, B., & Salgado, P. (2023). Numerical analysis of a FEM based on a time-primitive of the electric field for solving a nonlinear transient eddy current problem. Applied Numerical Mathematics, 192, 261-279. https://doi.org/10.1016/J.APNUM.2023.06.0090168-9274http://hdl.handle.net/10347/32399The aim of this paper is to analyze from a mathematical and a numerical point of view a formulation of a transient eddy current problem in terms of a time-primitive of the electric field in a bounded domain with ferromagnetic conductors. To this aim, we introduce a Lagrange multiplier to impose the free-divergence condition in the isolated domain. Thus, we obtain a nonlinear degenerate parabolic problem in mixed form and prove its well-posedness. Then, we propose a fully-discrete scheme by using an implicit Euler scheme for time-discretization and a finite element method based on edge and nodal elements for the spatial discretization. We prove quasi-optimal error estimates for the approximation and include some numerical examples to confirm the obtained theoretical results.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Nonlinear transient eddy current problemTime-primitive of the electric fieldNonlinear degenerate parabolic problemFinite elementsjournal article10.1016/j.apnum.2023.06.009open access