Abstract

ACEVEDO, Ramiro  and  LOAIZA, Gerardo. A Fully-Discrete Finite Element Approximation for the Eddy Currents Problem. ing.cienc. [online]. 2013, vol.9, n.17, pp.111-145. ISSN 1794-9165.

The eddy current model is obtained from Maxwell's equations by neglecting the displacement currents in the Ampère-Maxwell's law. The so-called ''A, V - A potential formulation'' is nowadays one of the most accepted formulations to solve the eddy current equations numerically, and Bíró & Valli 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 Bíró & 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.

Keywords : Transient eddy current model; potential formulation; fully-discrete approximation; finite elements; error estimates.

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