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Spring 2022 An integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions
Raphael Watschinger, Günther Of
J. Integral Equations Applications 34(1): 103-133 (Spring 2022). DOI: 10.1216/jie.2022.34.103

Abstract

While an integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions is available in the literature, a proof of this formula seems to be missing. Moreover, the available formula contains an integral term including the time derivative of the fundamental solution of the heat equation, whose interpretation is difficult at second glance. To fill these gaps, we provide a rigorous proof of a general version of the integration by parts formula and an alternative representation of the mentioned integral term, which is valid for a certain class of functions including the typical tensor-product discretization spaces.

Citation

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Raphael Watschinger. Günther Of. "An integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions." J. Integral Equations Applications 34 (1) 103 - 133, Spring 2022. https://doi.org/10.1216/jie.2022.34.103

Information

Received: 3 May 2021; Revised: 4 August 2021; Accepted: 17 August 2021; Published: Spring 2022
First available in Project Euclid: 11 April 2022

Digital Object Identifier: 10.1216/jie.2022.34.103

Subjects:
Primary: 45E10 , 65M38

Keywords: boundary element method , heat equation , hypersingular operator , integration by parts formula , space-time

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.34 • No. 1 • Spring 2022
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