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A Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equation

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posted on 2017-05-15, 13:54 authored by Lehel Banjai, Emmanuil H. Georgoulis, Oluwaseun Lijoka
A new space-time discontinuous Galerkin (dG) method utilizing special Trefftz polynomial basis functions is proposed and fully analyzed for the scalar wave equation in a second order formulation. The dG method considered is motivated by the class of interior penalty dG methods, as well as by the classical work of Hughes and Hulbert [Comput. Methods Appl. Mech. Engrg., 66 (1988), pp. 339-363; Comput. Methods Appl. Mech. Engrg., 84 (1990), pp. 327-348]. The choice of the penalty terms included in the bilinear form is essential for both the theoretical analysis and for the practical behavior of the method for the case of lowest order basis functions. A best approximation result is proven for this new space-time dG method with Trefftz-type basis functions. Rates of convergence are proved in any dimension and verified numerically in spatial dimensions d = 1 and d = 2. Numerical experiments highlight the effectivness of the Trefftz method in problems with energy at high frequencies.

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Citation

SIAM Journal on Numerical Analysis, 2017, 55 (1), pp. 63-86

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • VoR (Version of Record)

Published in

SIAM Journal on Numerical Analysis

Publisher

Society for Industrial and Applied Mathematics

issn

0036-1429

eissn

1095-7170

Acceptance date

2016-09-16

Copyright date

2017

Available date

2017-05-15

Publisher version

http://epubs.siam.org/doi/10.1137/16M1065744

Language

en

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