Summary
In this paper we apply a hybrid method to estimate a temporally and spatially varying diffusion coefficient in a parabolic system. This technique combines the output-least-squares- and the equation error method. The resulting optimization problem is solved by an augmented Lagrangian approach and convergence as well as rate of convergence proofs are provided. The stability of the estimated coefficient with respect to perturbations in the observation is guaranteed.
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Supported in part by the Fonds zur Förderung der wissenschaftlichen Forschung, Austria, under project S3206. K.K. also acknowledges support through AFOSR-F49620-86-C111
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Kunisch, K., Peichl, G. Estimation of a temporally and spatially varying diffusion coefficient in a parabolic system by an augmented Lagrangian technique. Numer. Math. 59, 473–509 (1991). https://doi.org/10.1007/BF01385792
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DOI: https://doi.org/10.1007/BF01385792