Non-dissipative space-time hp-discontinuous Galerkin method for the time-dependent Maxwell equations

A finite element method for the solution of the time-dependent Maxwell equations in mixed form is presented. The method allows for local hp-refinement in space and in time. To this end, a space-time Galerkin approach is employed. In contrast to the space-time DG method introduced in [1] test and trial spaces do not coincide. This allows for obtaining a non-dissipative method. To obtain an efficient implementation, a hierarchical tensor product basis in space and time is proposed. This allows to evaluate the local residual with a complexity of O(p4) and O(p5) for affine and non-affine elements, respectively.