A fully-discrete finite element approximation for the eddy currents problem

The eddy current model is obtained from Maxwell’s equations by neglecting the displacement currents in the Amp`ere-Maxwell’s law and it is commonly used in many problems in sciences, engineering and industry (e.g, in induction heating, electromagnetic braking, and power transformers). The so-called “A, V −A potential formulation” (B´ır´o & Preis [1]) is nowadays one of the most accepted formulations to solve the eddy current equations numerically, and B´ır´o & Valli [2] have recently provided its well-posedness and convergence analysis for the time-harmonic eddy current problem. The aim of this paper is to extend the analysis performed by B´ır´o & Valli to the general transient eddy current model. We provide a backward-Euler fully-discrete approximation based on nodal finite elements and we show that the resulting discrete variational problem is well posed. Furthermore, error estimates that prove optimal convergence are settled.

• Autores: Acevedo, Ramiro; Loaiza, Gerardo
• Fecha de publicación: 2013
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: eng
• OAI Identifier: oai:repository.eafit.edu.co:10784/14413
• Acceso en línea: http://hdl.handle.net/10784/14413
• Palabra clave: Transient Eddy Current Model; Potential Formulation; Fully-Discrete Approximation; finite Elements; Error Estimates; Modelo De Corriente Parásita Transitoria; Formulación Potencial; Aproximación Totalmente Discreta; Elementos Finitos; Estimaciones De Error
• License: Copyright (c) 2013 Ramiro Acevedo, Gerardo Loaiza