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Zbl 1063.65102
Yi, Zh.; Murio, D.A.
Source term identification in 1-D IHCP. (English)
[J] Comput. Math. Appl. 47, No. 12, 1921-1933 (2004). ISSN 0898-1221

Summary: We propose stable numerical solutions for the simultaneous identification of temperature, temperature gradient, and general source terms in the one-dimensional inverse heat conduction problem (IHCP).\par The numerical solution consists of a regularization procedure, based on the mollification method, and a marching scheme for the solution of the stabilized problem. The stability, error analysis and implementation of the algorithm are presented together with a set of numerical results.

MSC 2000:: *65M32 Inverse problems
35K05 Heat equation
35R30 Inverse problems for PDE
65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)
80A23 Inverse problems (thermodynamics)
80M20 Finite difference methods

Keywords: Discrete mollification; Identification of source terms; Finite differences; Space marching schemes; Parabolic equations; Stability; Inverse heat conduction problem; regularization; Error analysis; Algorithm; Numerical results

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