A projection penalization approach for the high order DG-FEM in the time domain

We investigate the Discontinuous Galerkin-Finite Element Method (DG-FEM) for the solution of Maxwell´s equations in the time domain. The charge conservation laws are known to be violated by this formulation, which consequently gives rise to spurious solutions in numerical simulations. It is however, possible to impose additional constrains within the framework of DG-FEM and thus obtain a “clean” spectrum of physical eigenvalues. In this work a penalization approach based on an orthogonal projection into a high order H(curl)-conforming approximation space is proposed. The method separates spurious from physical solution modes while maintaining accuracy and strict energy conservation.