Paper on a Non-dissipative space–time hp-discontinuous Galerkin method for the time-dependent Maxwell equations published in JCP

Our paper dealing with the PhD project of Martin Lilienthal has been published in JCP: Non-dissipative space–time hp-discontinuous Galerkin method for the time-dependent Maxwell equations. The abstract reads:

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 [Van der Vegt, JCP(182) 2002] 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 $$\mathcal{O}(p^4)$$ and $$\mathcal{O}(p^5)$$ for affine and non-affine elements, respectively.