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Time-adaptive FEM for distributed parameter identification in mathematical model of HIV infection with drug therapy

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Inverse Problems and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 120))

Abstract

We propose a time-adaptive finite element method for the solution of a parameter identification problem for ODE system which describes dynamics of primary HIV infection with drug therapy. We present framework of a posteriori error estimate in the Tikhonov functional and in the Lagrangian. We also formulate the time-mesh refinement recommendation and an adaptive algorithm to find optimal values of the distributed parameter in our identification problem.

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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 (2014) and the Russian Foundation for Basic Research (Grant 14-01-00477).

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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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Corresponding author

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. (2015). Time-adaptive FEM for distributed parameter identification in mathematical model of HIV infection with drug therapy. In: Beilina, L. (eds) Inverse Problems and Applications. Springer Proceedings in Mathematics & Statistics, vol 120. Springer, Cham. https://doi.org/10.1007/978-3-319-12499-5_8

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