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Title: A Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equation
Authors: Banjai, Lehel
Georgoulis, Emmanuil H.
Lijoka, Oluwaseun
First Published: 5-Jan-2017
Publisher: Society for Industrial and Applied Mathematics
Citation: SIAM Journal on Numerical Analysis, 2017, 55 (1), pp. 63-86
Abstract: 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.
DOI Link: 10.1137/16M1065744
ISSN: 0036-1429
eISSN: 1095-7170
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2017, Society for Industrial and Applied Mathematics. Deposited with reference to the publisher’s archiving policy available on the SHERPA/RoMEO website.
Appears in Collections:Published Articles, Dept. of Mathematics

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