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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.

MSC:

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
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References:

[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
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[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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