Identification of source terms in 2-D IHCP. (English) Zbl 1155.65376

Summary: We introduce a stable numerical space marching scheme based on discrete mollification – implemented as an automatic adaptive filter – for the approximate identification of temperature, temperature gradient, and source terms in the two-dimensional inverse heat conduction problem (IHCP).
The stability and error analysis of the algorithm, together with some numerical examples, are provided.


65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
80A23 Inverse problems in thermodynamics and heat transfer
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
47A52 Linear operators and ill-posed problems, regularization
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
Full Text: DOI


[1] Z. Yi and D.A. Murio, Source term identification in the 1-D IHCP, Computers Math. Applic.; Z. Yi and D.A. Murio, Source term identification in the 1-D IHCP, Computers Math. Applic. · Zbl 1063.65102
[2] Coles, C.; Murio, D. A., Simultaneous space diffusivity and source term reconstruction in 2D IHCP, Computers Math. Applic., 42, 12, 1549-1564 (2001) · Zbl 1005.65106
[3] Mejia, C. E.; Murio, D. A., Mollified hyperbolic method for coefficient identification problems, Computers Math. Applic., 26, 5, 1-12 (1993) · Zbl 0789.65090
[4] Murio, D. A., (Woodbury, K., Mollification and Space Marching, Inverse Engineering Handbook (2002), CRC Press: CRC Press Boston, MA), 219-326, Chapter 4 · Zbl 1071.65130
[5] Cannon, J. R.; Du Chateau, P., Inverse problems for an unknown source in the heat equation, Journal of Mathematical Analysis and Applications, 75, 465-485 (1980) · Zbl 0448.35085
[6] Ewing, R.; Lin, T., Parameter identification problems in single-phase and two-phase flow, (International Series of Numerical Mathematics, Volume 91 (1989), Birkhäuser Verlag: Birkhäuser Verlag Boca Ratón, FL), 85-108 · Zbl 0686.93016
[7] Nanda, A.; Das, P., Determination of the source term in the heat conduction equation, Inverse Problems, 12, 325-339 (1996) · Zbl 0851.35135
[8] Isakov, V., Inverse Source Problems (1990), American Mathematical Society: American Mathematical Society Basel · Zbl 0721.31002
[9] Murio, D. A.; Mejia, C. E.; Zhan, S., Discrete mollification and automatic numerical differentiation, Computers Math. Applic., 35, 5, 1-16 (1998) · Zbl 0910.65010
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