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Parameter identification for nonlinear elliptic-parabolic systems with application in lithium-ion battery modeling

Abstract

In this paper the authors consider a parameter estimation problem for a nonlinear systems, which consists of one parabolic equation for the concentration and two elliptic equations for the potentials. The measurements are given as boundary values for one of the potentials. For its numerical solution the Gauss Newton method is applied. To speed up the solution process, a reduced-order approach based on proper orthogonal decomposition is utilized, where the accuracy is controlled by error estimators. Parameters, which can not be identified from the measurements, are identified by the subset selection method with \(QR\) pivoting. Numerical examples show the efficiency of the proposed approach.

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Acknowledgments

The authors gratefully acknowledges support by the German Science Funds Numerical and Analytical Methods for Elliptic-Parabolic Systems Appearing in the Modeling of Lithium-Ion Batteries (Excellence Initiative) and DFG grant VO 1658/2-1 A-posteriori-POD Error Estimators for Nonlinear Optimal Control Problems governed by Partial Differential Equations

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Correspondence to Stefan Volkwein.

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Lass, O., Volkwein, S. Parameter identification for nonlinear elliptic-parabolic systems with application in lithium-ion battery modeling. Comput Optim Appl 62, 217–239 (2015). https://doi.org/10.1007/s10589-015-9734-8

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  • DOI: https://doi.org/10.1007/s10589-015-9734-8

Keywords

  • Proper orthogonal decomposition
  • Parameter estimation
  • A-posteriori error estimates
  • subset selection method
  • Elliptic-parabolic systems