Non-Dissipative Space-Time hp-discontinuous Galerkin Method for the Time-Dependent Maxwell Equations

by M Lilienthal, S M Schnepp, T Weiland
Abstract:
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 textitJ.J.W. van der Vegt, H. van der Ven, JCP 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.
Reference:
Non-Dissipative Space-Time hp-discontinuous Galerkin Method for the Time-Dependent Maxwell Equations (M Lilienthal, S M Schnepp, T Weiland), In Journal of Computational Physics (In Press), 2014.
Bibtex Entry:
@article{Lilienthal:2013vx,
author = {Lilienthal, M and Schnepp, S M and Weiland, T},
title = {{Non-Dissipative Space-Time hp-discontinuous Galerkin Method for the Time-Dependent Maxwell Equations}},
journal = {Journal of Computational Physics (In Press)},
year = {2014},
abstract = {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 textit{J.J.W.~van der Vegt, H.~van der Ven, JCP 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.},
url = {http://www.sciencedirect.com/science/article/pii/S0021999114005087}
}

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