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

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Lehel Banjai, Emmanuil H. Georgoulis, Oluwaseun Lijoka

Numerical Analysis · Submitted 6 Oct 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Numerical experiments highlight the effectiveness of the Trefftz method in problems with energy at high frequencies.

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arXiv ID1610.01878 (version 1)
Pith ID3BNNWLCT, Pith's permanent record of this paper and its review
CitationEmmanuil H. Georgoulis, Lehel Banjai, Oluwaseun Lijoka. "A Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equation." arXiv:1610.01878 (2016). https://pith.science/paper/3BNNWLCT
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,926 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.35 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.34 · compares with prior results 0.23 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

A new space-time discontinuous Galerkin (dG) method utilising special Trefftz polynomial basis functions is proposed and fully analysed 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. The choice of the penalty terms included in the bilinear form is essential for both the theoretical analysis and for the practical behaviour 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 effectiveness of the Trefftz method in problems with energy at high frequencies.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A new space-time discontinuous Galerkin (dG) method utilising special Trefftz polynomial basis functions is proposed and fully analysed for the scalar wave equation in a second order formulation. contribution 0.99 0.95 0.25 asserted 1.00
s1 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. background 0.94 0.14 0.02 asserted 1.00
s2 The choice of the penalty terms included in the bilinear form is essential for both the theoretical analysis and for the practical behaviour of the method for the case of lowest order basis functions. method 0.75 0.41 0.06 asserted 1.00
s3 A best approximation result is proven for this new space-time dG method with Trefftz-type basis functions. result 0.93 0.95 0.26 asserted 1.00
s4 Rates of convergence are proved in any dimension and verified numerically in spatial dimensions $d = 1$ and $d = 2$. result 0.97 0.96 0.24 asserted 1.00
s5 Numerical experiments highlight the effectiveness of the Trefftz method in problems with energy at high frequencies. result 0.85 0.93 0.24 asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.99.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

A new space-time discontinuous Galerkin (dG) method utilising special Trefftz polynomial basis functions is proposed and fully analysed 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. The choice of the penalty terms included in the bilinear form is essential for both the theoretical analysis and for the practical behaviour 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 effectiveness of the Trefftz method in problems with energy at high frequencies.

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