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Time-Adaptive FEM for Distributed Parameter Identification in Biological Models

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Applied Inverse Problems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 48))

Abstract

We propose a time-adaptive finite element method for the solution of a parameter identification problem for ODE which describes dynamical systems of biological models. We present framework of a posteriori error estimate in the Tikhonov functional, in Lagrangian, and in the reconstructed function. We also present time-mesh relaxation property in the adaptivity and formulate the time-mesh refinement recommendation and an adaptive algorithm which can be used to find optimal values of the distributed parameters in biological models.

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Acknowledgements

This research was supported by the Swedish Research Council, the Swedish Foundation for Strategic Research (SSF) through the Gothenburg Mathematical Modelling Centre (GMMC), the Swedish Institute, Visby Program, the program of the Russian Academy of Sciences “Basic Research for Medicine,” and the Russian Foundation for Basic Research (Grant 11-01-00117).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University, SE-42196, Gothenburg, Sweden

    Larisa Beilina

  2. Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia

    Irina Gainova

Authors
  1. Larisa Beilina
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  2. Irina Gainova
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Correspondence to Larisa Beilina .

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Editors and Affiliations

  1. Department of Mathematical Sciences, Chalmers University of Technology Gothenburg University, Gothenburg, Sweden

    Larisa Beilina

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Beilina, L., Gainova, I. (2013). Time-Adaptive FEM for Distributed Parameter Identification in Biological Models. In: Beilina, L. (eds) Applied Inverse Problems. Springer Proceedings in Mathematics & Statistics, vol 48. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7816-4_3

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