RT Journal Article
T1 Numerical analysis of a FEM based on a time-primitive of the electric field for solving a nonlinear transient eddy current problem.
A1 Acevedo, Ramiro
A1 Gómez, Christian
A1 López-Rodríguez, Bibiana
A1 Salgado Rodríguez, María del Pilar
K1 Nonlinear transient eddy current problem
K1 Time-primitive of the electric field
K1 Nonlinear degenerate parabolic problem
K1 Finite elements
AB The 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.
PB Elsevier
SN 0168-9274
YR 2023
FD 2023
LK http://hdl.handle.net/10347/32399
UL http://hdl.handle.net/10347/32399
LA eng
NO Acevedo, 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.2023.06.009
NO R. Acevedo and C. Gómez were partially supported by Universidad del Cauca through project VRI ID 5869. B. López-Rodríguez was partially supported by Universidad Nacional de Colombia through Hermes project 11982. B. López-Rodríguez and P. Salgado were supported by FEDER, Ministerio de Ciencia e Innovación through the research project PID2021-122625OB-I00 and, by Xunta de Galicia (Spain) research project GI-1563 ED431C 2021/15.
DS Minerva
RD 28 abr 2026