Transient 3D magnetic field simulations with combined space and time mesh adaptivity for lowest order Whitney finite element formulations

Transient quasistatic magnetic fields are described by a degenerate parabolic initial-boundary value problems which can be considered as dynamical systems of non-linear differential-algebraic equations (DAE) of index 1. A common approach in established simulation tools for solving this problem is the method of lines where the space is adaptively discretised at the beginning of the simulation and then kept fixed within the adaptive time integration of the time-dependent equation. This approach, however, fails to take into account changes of the solution when eddy currents may appear or vanish depending on the external current excitation. Here, for this type of problem adaptive strategies in space and time are considered.