Fully discrete approximation methods for the estimation of parabolic systems and boundary parameters
A spatially and temporally discrete approximation scheme is developed for the identification of a class of semilinear parabolic systems with unknown boundary parameters. The identification problem is formulated as a least squares fit to data subject to an equivalent representation for the dynamics in the form of an abstract evolution equation. An approximation method, based on Galerkin's method with cubic splines and Padé approximation of exponentials, is constructed. A sequence of approximating identification problems results, the solutions of which are shown to exist, and in a certain sense approximate solutions of the original identification problem. Numerical results for two examples, both based on actual experimental data, are included.
scientific article; zbMATH DE number 3988670
scientific article