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Most Downloaded Articles
- Conference announcement “Inverse and Ill-Posed Problems of Mathematical Physics” dedicated to the 80th birthday of Academician M. M. Lavrentiev
- The inverse spectral problem for the Sturm–Liouville operator with discontinuous potential by Sedipkov, Aydys A.
- Chemnitz Symposium on Inverse ProblemsChemnitz, Germany, September 27–28, 2007 by Hofmann, B.
Numerical solution of inverse heat conduction problems in two spatial dimensions
11. University of Siegen, Department of Mathematics, Walter-Flex-Str. 3, 57068 Siegen, Germany.
32. Hanoi Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam.
53. University of Siegen, Department of Mathematics, Walter-Flex-Str. 3, 57068 Siegen, Germany.
74. University of Siegen, Department of Mathematics, Walter-Flex-Str. 3, 57068 Siegen, Germany.
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 15, Issue 2, Pages 181–198, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2007.010, May 2007
- Published Online:
Inverse heat conduction problems (IHCPs) have been extensively studied over the last 50 years. They have numerous applications in many branches of science and technology. The problem consists in determining the temperature and heat flux at inaccessible parts of the boundary of a 2- or 3-dimensional body from corresponding data — called 'Cauchy data' — on accessible parts of the boundary. It is well known that IHCPs are severely illposed which means that small perturbations in the data may cause extremely large errors in the solution. In this contribution we first present the problem and show examples of calculations for 2-dimensional IHCP's where the direct problems are solved with the Finite Element package DEAL. As solution procedure we use Tikhonov's regularization in combination with the conjugate gradient method.