A numerical technique for the estimation of the diffusion coefficient in parabolic systems

A hybrid method for estimating a temporally and spatially varying diffusion coefficient in a parabolic system is presented. This technique combines the output-least-squares and the equation error method. The resulting optimization problem is solved by an augmented Lagrangian approach. Convergence of the algorithm and stability of the estimated coefficient with respect to perturbations in the observation are discussed. Comments are made regarding the implementation of the algorithm, and the theory is illustrated by means of a numerical example.<
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