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

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

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.
Originalspracheenglisch
Seiten (von - bis)103-133
Seitenumfang31
FachzeitschriftJournal of Integral Equations and Applications
Jahrgang34
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - 2022

ASJC Scopus subject areas

  • Angewandte Mathematik
  • Numerische Mathematik

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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