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Adaptive Finite Elements for Output-Oriented Model Calibration

In: Modeling, Simulation and Optimization of Complex Processes

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  • Boris Vexler

    (Universität Heidelberg, Institut für Angewandte Mathematik)

Abstract

Summary We consider the problem of model calibration involving partial differential equations. The problem is formulated as a parameter identification problem with finite number of unknown parameters, which can occur in the differential operator as well as in the boundary conditions. The finite element discretization on locally refined meshes is adaptively chosen with regard to a goal functional, which corresponds to a quantity of interest (output) of the state equation. An a posteriori error estimator for the error in the goal functional is derived. It is used for the quantitative error control and successive improvement of the accuracy by appropriate mesh refinement. Numerical examples illustrate the behavior of the method.

Suggested Citation

  • Boris Vexler, 2005. "Adaptive Finite Elements for Output-Oriented Model Calibration," Springer Books, in: Hans Georg Bock & Hoang Xuan Phu & Ekaterina Kostina & Rolf Rannacher (ed.), Modeling, Simulation and Optimization of Complex Processes, pages 523-538, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27170-3_39
    DOI: 10.1007/3-540-27170-8_39
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