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\title{An Efficient Dynamic $hp$-Discontinuous Galerkin Formulation for Time-Domain Electromagnetics}
\tocauthor{S. Schnepp} \author{} \institute{}
{\large Sascha Schnepp}\\
Graduate School CE, TU Darmstadt\\
The discontinuous Galerkin method (DGM) \cite{reed} received considerable development over the past two decades leading it to a mature state. In many cases the DGM is applied in a spectral-like manner on static meshes using a fixed approximation order throughout all elements. The strictly local support of the basis functions, however, renders the method highly suitable for adapting the local element size, $h$, as well as the local approximation order, $p$, in an element-wise fashion based on the local solution behavior.
In this talk a DG formulation on hexahedral meshes \cite{cohen} supporting dynamic $hp$-refinement \cite{houston} containing high-level hanging nodes and anisotropic refinement in both, $h$ and $p$, is presented. During the development special care of the computational efficiency of the basic algorithm and the adaptation procedures has been taken. The method is especially successful for multi-scale problems, where the adaptive approach leads to significant savings in computational resources and time.
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