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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 tensorproduct discretization spaces.
Original language  English 

Pages (fromto)  103133 
Number of pages  31 
Journal  Journal of Integral Equations and Applications 
Volume  34 
Issue number  1 
DOIs  
Publication status  Published  2022 
Keywords
 Boundary element method
 Heat equation
 Hypersingular operator
 Integration by parts formula
 Spacetime
ASJC Scopus subject areas
 Applied Mathematics
 Numerical Analysis
Fields of Expertise
 Information, Communication & Computing
Treatment code (Nähere Zuordnung)
 Basic  Fundamental (Grundlagenforschung)
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 1 Finished

FWF  Besthea  Spacetime boundary element methods for the heat equation
Of, G. & Watschinger, R.
1/03/19 → 30/11/22
Project: Research project