Appropriate finite-element formulations for 3-D electromagnetic-field problems

This paper deals with the appropriate finite-element (FE) formulations of three-dimensional electromagnetic-field problems. The magnetic vector potential is used as the field variable and two variational formulations for the FE discretization with Lagrange (nodal) as well as Nedelec (edge) FEs are discussed. We will especially focus on the problems arising by using nodal FEs and will demonstrate the correct approximation by applying a special weighting within the divergence integral.