Two variants of magnetic diffusivity stabilized finite element methods for the magnetic induction equation

We consider the time-dependent magnetic induction model where the sought magnetic field interacts with a prescribed velocity field. This coupling results in an additional force term and time dependence in Maxwell's equation. We propose two different magnetic diffusivity stabilized continuous nodal-based finite element methods for this problem. The first formulation simply adds artificial magnetic diffusivity to the partial differential equation, whereas the second one uses a local projected magnetic diffusivity as stabilization. We describe those methods and analyze them semi-discretized in space to get bounds on stabilization parameters where we distinguish equal-order elements and Taylor-Hood elements. Different numerical experiments are performed to illustrate our theoretical findings.