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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.
|Number of pages||31|
|Journal||Journal of Integral Equations and Applications|
|Publication status||Published - 2022|
- Boundary element method
- Heat equation
- Hypersingular operator
- Integration by parts formula
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 - Space-time boundary element methods for the heat equation
Of, G. & Watschinger, R.
1/03/19 → 30/11/22
Project: Research project