Numerical solution of transient eddy current problems with input current intensities as boundary data

The aim of this paper is to analyse a numerical method to solve transient eddy current problems with input current intensities as data, formulated in terms of the magnetic field in a bounded domain including conductors and dielectrics. To this end, we introduce a time-dependent weak formulation and prove its well-posedness. We propose a finite element method for space discretization based on the Nedelec edge elements on tetrahedral meshes, for which we obtain error estimates. Then we introduce a backward Euler scheme for time discretization and prove error estimates for the fully discrete problem, too. Furthermore, a magnetic scalar potential is introduced to deal with the curl-free condition in the dielectric domain, which leads to an important saving in computational effort. Finally, the method is applied to solve two problems: a test with a known analytical solution and an application to electromagnetic forming.