The boundaryelement method for the determination of a heat source dependent on one variable
 Adrian Farcas,
 Daniel Lesnic
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This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions of the direct problem and a supplementary condition, called an overdetermination. In this problem, if the heat source is taken to be spacedependent only, then the overdetermination is the temperature measurement at a given single instant, whilst if the heat source is timedependent only, then the overdetermination is the transient temperature measurement recorded by a single thermocouple installed in the interior of the heat conductor. These measurements ensure that the inverse problem has a unique solution, but this solution is unstable, hence the problem is illposed. This instability is overcome using the Tikhonov regularization method with the discrepancy principle or the Lcurve criterion for the choice of the regularization parameter. The boundaryelement method (BEM) is developed for solving numerically the inverse problem and numerical results for some benchmark test examples are obtained and discussed
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 Title
 The boundaryelement method for the determination of a heat source dependent on one variable
 Journal

Journal of Engineering Mathematics
Volume 54, Issue 4 , pp 375388
 Cover Date
 20060401
 DOI
 10.1007/s1066500590230
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 boundaryelement method
 heat source
 inverse problems
 parabolic equation
 Industry Sectors
 Authors

 Adrian Farcas ^{(1)}
 Daniel Lesnic ^{(2)}
 Author Affiliations

 1. BP Institute, University of Cambridge, Cambridge, CB3 0EZ, UK
 2. Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK