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Authors: Frühauf, Florian
Gebauer, Bastian
Scherzer, Otmar
Title: Detecting interfaces in a parabolic-elliptic problem from surface measurements
Online publication date: 25-Nov-2008
Year of first publication: 2007
Language: english
Abstract: Assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic-elliptic interface problem. In this work we aim to detect these interfaces from thermal measurements on the surface of the body. We deduce an equivalent variational formulation for the parabolic-elliptic problem and give a new proof of the unique solvability based on Lions’s projection lemma. For the case that the heat conductivity is higher inside the inclusions, we develop an adaptation of the factorization method to this time- dependent problem. In particular this shows that the locations of the interfaces are uniquely determined by boundary measurements. The method also yields to a numerical algorithm to recover the inclusions and thus the interfaces. We demonstrate how measurement data can be simulated numerically by a coupling of a finite element method with a boundary element method, and finally we present some numerical results for the inverse problem.
DDC: 510 Mathematik
510 Mathematics
Institution: Johannes Gutenberg-Universität Mainz
Department: FB 08 Physik, Mathematik u. Informatik
Place: Mainz
URN: urn:nbn:de:hebis:77-17918
Version: Published version
Publication type: Zeitschriftenaufsatz
License: In Copyright
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Journal: SIAM Journal on numerical analysis
Pages or article number: 810
Issue date: 2007
ISSN: 1095-7170
Publisher URL:
Publisher DOI: 10.1137/050641545
Appears in collections:JGU-Publikationen

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