Towards a Fully Space-Time Adaptive FEM for Magnetoquasistatics

This paper is concerned with fully space-time adaptive magnetic field computations. We describe a Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell´s equations on unstructured 3-D tetrahedral grids. Spatial discretization is done by employing hierarchical tetrahedral -conforming elements proposed by Ainsworth and Coyle. For the time discretization, we use a newly constructed one-step Rosenbrock method ROS3PL with third order accuracy in time. Adaptive mesh refinement and coarsening are based on hierarchical error estimators especially designed for Rosenbrock methods. An embedding technique is applied to get efficiency in time through variable time steps. Finally, we present numerical results for the benchmark problem TEAM 7.