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The eddy current model is obtained from Maxwell’s equations by neglecting the displacement currents in the Ampere-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 Biro & 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 Biro & 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.

A Fully-Discrete Finite Element Approximation for the Eddy Currents Problem