Non-dissipative space-time $hp$-discontinuous Galerkin method for the time-dependent Maxwell Equations
For computational electromagnetics, this method offers a non-dissipative, high-order accurate approach with local refinement capabilities, though it is an incremental improvement over existing space-time DG methods.
The paper presents a space-time discontinuous Galerkin method for time-dependent Maxwell equations that allows local hp-refinement in space and time, achieving a non-dissipative scheme with efficient implementation via hierarchical tensor product basis, reducing residual evaluation complexity to O(p^4) for affine and O(p^5) for non-affine elements.
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 \cite{vegt_space_2002} test and trial space do not coincide. This allows for obtaining a non-dissipative method. In order to obtain an efficient implementation, a hierarchical tensor product basis in space and time is proposed. In particular it 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.