Dear Andreas,
This is a specialized application domain; I am not sure if anyone here has done induction heating but I will do my best to try and point you in a useful direction.
1. I don't think we have any examples in the documentation about how to solve this problem. However, there are other examples of heat transfer in papers citing deal.II: check out the list at
2. For electromagnetism you probably want to use the Nedelec_SZ element. These elements tend to be very complicated so it is probably best to use one that is already in the library.
3. I don't know how to couple the electromagnetic field to the thermal problem.
Thanks,
David Wells