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Residual-minimization least-squares method for inverse heat conduction. (English) Zbl 0858.65098

Summary: A numerical method is systematically developed for resolving an inverse heat conduction problem in the presence of noisy discrete data. This paper illustrates the effect of imposing constraints on the unknown function of interest. A Volterra integral equation of the first kind is derived and used as the starting point for residual-minimization, least squares methodology. Symbolic manipulation is exploited for purposes of augmenting the computational methodology.
Preliminary indications suggest that the imposition of physical constraints on the system drastically reduces the level of mathematical sophistication needed for accurately approximating the unknown function of interest. These constraints are actually available in many design studies or from models which are derived by physical processes.

MSC:

65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65R20 Numerical methods for integral equations
45D05 Volterra integral equations
35R30 Inverse problems for PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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