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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.

65M30Improperly posed problems (IVP of PDE, numerical methods)
35K05Heat equation
65R20Integral equations (numerical methods)
45D05Volterra integral equations
35R30Inverse problems for PDE
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)