Discontinuous Galerkin methods with Trefftz approximations

We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space–time Trefftz basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The bas...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2014-11, Vol.270, p.211-222
Main Authors: Kretzschmar, Fritz, Schnepp, Sascha M., Tsukerman, Igor, Weiland, Thomas
Format: Article
Language:English
Subjects:
Discontinuous Galerkin method
Electrodynamics
Finite element method
Higher order time integration
Trefftz method
Wave propagation
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Summary:We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space–time Trefftz 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 arbitrarily high order and we demonstrate spectral convergence in the space–time L2-norm. Therefore high order time integration is an inherent property of the method and clearly sets it apart from methods that employ a high order approximation in space only.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2014.01.033