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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.

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
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