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
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-309
URN:	urn:nbn:de:hebis:77-17918
Version:	Published version
Publication type:	Zeitschriftenaufsatz
License:	In Copyright
Information on rights of use:	https://rightsstatements.org/vocab/InC/1.0/
Journal:	SIAM Journal on numerical analysis 45 2
Pages or article number:	810 836
Issue date:	2007
ISSN:	1095-7170
Publisher URL:	https://doi.org/10.1137/050641545
Publisher DOI:	10.1137/050641545
Appears in collections:	JGU-Publikationen