Towards coercive boundary element methods for the wave equation

Olaf Steinbach; Carolina Urzúa–Torres; Marco Zank

doi:10.1216/JIE.2022.34.501

Towards coercive boundary element methods for the wave equation

Olaf Steinbach^*, Carolina Urzúa–Torres, Marco Zank

^*Corresponding author for this work

Numerical Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

We discuss the ellipticity of the single layer boundary integral operator for the wave equation in one space dimension. This result not only generalizes the well-known ellipticity of the energetic boundary integral formulation in L², but it also turns out to be a particular case of a recent result on the inf-sup stability of boundary integral operators for the wave equation. Instead of the time derivative in the energetic formulation, we use a modified Hilbert transformation, which allows us to stay in Sobolev spaces of the same order.

Original language	English
Pages (from-to)	501-515
Number of pages	15
Journal	Journal of Integral Equations and Applications
Volume	34
Issue number	4
DOIs	https://doi.org/10.1216/JIE.2022.34.501
Publication status	Published - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Ellipticity
Modified hilbert transformation
Single layer boundary integral operator
Wave equation

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10.1216/JIE.2022.34.501

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title = "Towards coercive boundary element methods for the wave equation",

abstract = "We discuss the ellipticity of the single layer boundary integral operator for the wave equation in one space dimension. This result not only generalizes the well-known ellipticity of the energetic boundary integral formulation in L2, but it also turns out to be a particular case of a recent result on the inf-sup stability of boundary integral operators for the wave equation. Instead of the time derivative in the energetic formulation, we use a modified Hilbert transformation, which allows us to stay in Sobolev spaces of the same order.",

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AU - Zank, Marco

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KW - Modified hilbert transformation

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KW - Wave equation

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Towards coercive boundary element methods for the wave equation

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Keywords

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