Autoren:	Frühauf, Florian Gebauer, Bastian Scherzer, Otmar
Titel:	Detecting interfaces in a parabolic-elliptic problem from surface measurements
Online-Publikationsdatum:	25-Nov-2008
Erscheinungsdatum:	2007
Sprache des Dokuments:	Englisch
Zusammenfassung/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-Sachgruppe:	510 Mathematik 510 Mathematics
Veröffentlichende Institution:	Johannes Gutenberg-Universität Mainz
Organisationseinheit:	FB 08 Physik, Mathematik u. Informatik
Veröffentlichungsort:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-309
URN:	urn:nbn:de:hebis:77-17918
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Nutzungsrechte:	Urheberrechtsschutz
Informationen zu den Nutzungsrechten:	https://rightsstatements.org/vocab/InC/1.0/
Zeitschrift:	SIAM Journal on numerical analysis 45 2
Seitenzahl oder Artikelnummer:	810 836
Erscheinungsdatum:	2007
ISSN:	1095-7170
URL der Originalveröffentlichung:	https://doi.org/10.1137/050641545
DOI der Originalveröffentlichung:	10.1137/050641545
Enthalten in den Sammlungen:	JGU-Publikationen