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.
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Vexler, B. (2005). Adaptive Finite Elements for Output-Oriented Model Calibration. In: Bock, H.G., Phu, H.X., Kostina, E., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27170-8_39
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DOI: https://doi.org/10.1007/3-540-27170-8_39
Publisher Name: Springer, Berlin, Heidelberg
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