The aim of this paper is to propose and analyze a numerical method to solve a timedependent eddy current problem in a domain containing moving non magnetic conductors. To this
end, we choose a formulation in terms of the magnetic field, what leads to a parabolic problem
for which we prove an existence result. For space discretization, we propose a finite element
method based on Nédélec edge elements on a mesh that remains fixed over the time. The curl-free
constraint in the dielectric domain is relaxed by means of a penalty strategy that can be easily
implemented, without the need that the mesh fits the moving conducting and dielectric domains.
For time discretization, we use a backward Euler scheme. We report some numerical results.
First, we solve a test problem with a known analytical solution, which allows us to assess the
convergence of the method as the penalization and discretization parameters go to zero. Finally,
we solve a problem with cylindrical symmetry, which allows us to compare the results with those
obtained with an axisymmetric code.