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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:
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