The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations

This paper deals with the numerical solution of the time dependent Maxwell equations. In particular, we are interested in time integration of the three-dimensional Maxwell equations discretized in space by Nedelec’s edge finite elements [28,29]. Nedelec’s edge and face elements have a number of attractive properties (as e.g. automatic satisfaction of the proper continuity requirements across the boundaries between different materials) and are a standard tool in the numerical treatment of the Maxwell equations [25].We emphasize, however, that the time integration techniques presented in this paper are applicable to any space-discretized second order wave equation(s).