• Maxwell equations;
  • discontinuous Galerkin;
  • time domain

[1] 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 method which consequently gives rise to spurious numerical solutions. It is, however, possible to introduce additional constrains in the formulation which impose charge conservation either exactly or approximately. In this work, a new approach based on a topological orthogonal projector into a high-order H(curl)-conforming approximation space is proposed. Using this approach we derive a constrained DG-FEM formulation which is strictly free of spurious modes. Furthermore, we construct a time domain penalization scheme which allows to separate the spurious modes related to unphysical charges from the physical solutions while maintaining accuracy and energy conservation.