Time-Adaptive FEM for Distributed Parameter Identification in Biological Models
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.
KeywordsHuman Immunodeficiency Virus Type Mesh Refinement Tikhonov Regularization Posteriori Error Estimate Relaxation Property
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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