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arXiv · 1302.6459

Discontinuous Galerkin Methods with Trefftz Approximation

Fritz Kretzschmar·Sascha Schnepp·Igor Tsukerman·Thomas Weiland
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Abstract

We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space-time Trefftz-type basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The basis functions can be of arbitrary high order, and we demonstrate spectral convergence in the $\Lebesgue_2$-norm. In this context, spectral convergence is obtained with respect to the approximation error in the entire space-time domain of interest, i.e. in space and time simultaneously. Formulating the approximation in terms of a space-time Trefftz basis makes high order time integration an inherent property of the method and clearly sets it apart from methods, that employ a high order approximation in space only.

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Fritz Kretzschmar, Sascha Schnepp, Igor Tsukerman, Thomas Weiland. 2013-02-26. Discontinuous Galerkin Methods with Trefftz Approximation. https://doi.org/10.1016/j.cam.2014.01.033

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