Journal of Engineering Mathematics

, Volume 54, Issue 4, pp 375–388

The boundary-element method for the determination of a heat source dependent on one variable


DOI: 10.1007/s10665-005-9023-0

Cite this article as:
Farcas, A. & Lesnic, D. J Eng Math (2006) 54: 375. doi:10.1007/s10665-005-9023-0


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 space-dependent only, then the overdetermination is the temperature measurement at a given single instant, whilst if the heat source is time-dependent 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 ill-posed. This instability is overcome using the Tikhonov regularization method with the discrepancy principle or the L-curve criterion for the choice of the regularization parameter. The boundary-element method (BEM) is developed for solving numerically the inverse problem and numerical results for some benchmark test examples are obtained and discussed


boundary-element method heat source inverse problems parabolic equation 

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.BP InstituteUniversity of CambridgeCambridgeUK
  2. 2.Department of Applied MathematicsUniversity of LeedsLeedsUK