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  • 1
    Electronic Resource
    Electronic Resource
    Fully discrete approximation methods for the estimation of parabolic systems and boundary parameters (1986)
    Springer
    Acta applicandae mathematicae 7 (1986), S. 1-34 
    Details
    ISSN: 1572-9036
    Keywords: 41A15 ; 65N30 ; Parabolic systems ; parameter estimation ; approximation methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A spatially and temporally discrete numerical 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. Finite-dimensional difference equation state approximations are constructed using a cubic spline-based, Galerkin method and the Padé rational function approximations to the exponential. A sequence of approximating identification problems result, the solutions of which are shown to exist and, in a certain sense, approximate solutions to the original identification problem. Numerical results for two examples, one involving the modeling of biological mixing in deep sea sediment cores, and the other, the estimation of transport parameters for indoor mixing, are discussed. In both examples, the identification is based upon actual experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046975
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems (1991)
    Springer
    Applied mathematics & optimization 24 (1991), S. 233-256 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We develop an abstract framework and convergence theory for Galerkin approximation for inverse problems involving the identification of nonautonomous, in general nonlinear, distributed parameter systems. We provide a set of relatively easily verified conditions which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite-dimensional identification problems. Our approach is based upon the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasi-linear elliptic operators along with some applications and numerical results are presented and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01447744
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    Paper (German National Licenses)
    Fulltext
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