Representation of current density in a three-dimensional hierarchical edge finite element method solving directly for the magnetic field

The paper presents developments on an edge element method that is well suited to estimate eddy currents, although it primarily solves for the magnetic field. Basis functions are added hierarchically to the approximation spaces in order to improve the representation of current density, and also the magnetic field. Several opportunities for exploiting the elements in a computationally economical way exist, and one of these is demonstrated on a benchmark problem