Non-dissipative space-time $hp$-discontinuous Galerkin method for the time-dependent Maxwell Equations
Numerical Analysis
2014-12-18 v2 Computational Physics
Abstract
A finite element method for the solution of the time-dependent Maxwell equations in mixed form is presented. The method allows for local -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 and for affine and non-affine elements, respectively.
Cite
@article{arxiv.1307.5310,
title = {Non-dissipative space-time $hp$-discontinuous Galerkin method for the time-dependent Maxwell Equations},
author = {Martin Lilienthal and Sascha M. Schnepp and Thomas Weiland},
journal= {arXiv preprint arXiv:1307.5310},
year = {2014}
}