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Iteratively Regularized Gauss-Newton Methods under Random Noise Read chapter Read first chapter

2015 | OriginalPaper | Chapter

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

Authors : Larisa Beilina, Irina Gainova

Published in: Inverse Problems and Applications

Publisher: Springer International Publishing

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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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previous chapter Reconstruction of Dielectric Constants in a Cylindrical Waveguide
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Literature
1.
Bakushinskii, A.B., Kokurin, M.Y.: Iterative Methods for Approximate Solution of Inverse Problems. Springer, New York (2004)
2.
Bangerth, W., Joshi, A.: Adaptive finite element methods for the solution of inverse problems in optical tomography. Inverse Probl. 24, 03401–1 (2008)CrossRefMathSciNet
3.
Becker, R., Rannacher, R.: An optimal control approach to a posteriori error estimation in finite element method. Acta. Numer. 10, 1–102 (2001)CrossRefMATHMathSciNet
4.
Beilina, L.: Adaptive finite element method for a coefficient inverse problem for the Maxwell’s system. Appl. Anal. 90, 1461–1479 (2011)CrossRefMATHMathSciNet
5.
Beilina, L., Gainova, I.: Time-adaptive FEM for distributed parameter identification in biological models. Appl. Inverse Probl. Springer Proc. Math. Stat. 48, 37–50 (2013)
6.
Beilina, L., Johnson, C.: A hybrid FEM/FDM method for an inverse scattering problem.In: Numerical Mathematics and Advanced Applications—ENUMATH 2001. Springer-Verlag, Berlin (2001)
7.
Beilina, L., Johnson, C.: A posteriori error estimation in computational inverse scattering. Math. Models Methods Appl. Sci. 15, 23–37 (2005)CrossRefMATHMathSciNet
8.
Beilina, L., Klibanov, M.V.: Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems. Springer, New York (2012)CrossRefMATH
9.
Beilina, L., Klibanov, M.V., Kokurin, M.Y.: Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem. J. Math. Sci. 167, 279–325 (2010)CrossRefMATHMathSciNet
10.
Eriksson, K., Estep, D., Johnson, C.:Calculus in Several Dimensions. Springer, Berlin (2004)
11.
Feng, T., Yan, N., Liu, W.: Adaptive finite element methods for the identification of distributed parameters in elliptic equation. Adv. Comput. Math. 29, 27–53 (2008)CrossRefMATHMathSciNet
12.
Griesbaum, A., Kaltenbacher, B., Vexler, B.: Efficient computation of the Tikhonov regularization parameter by goal-oriented adaptive discretization. Inverse Probl. 24, 02502–5 (2008)CrossRefMathSciNet
13.
Kaltenbacher, B., \refsn Neubauer, A., Scherzer, O.: Iterative Regularization Methods for Nonlinear Ill-Posed Problems. de Gruyter, New York (2008)
14.
Kaltenbacher, B., Krichner, A., Vexler, B.: Adaptive discretizations for the choice of a Tikhonov regularization parameter in nonlinear inverse problems. Inverse Probl. 27, 12500–8 (2011)
15.
Koshev, N., Beilina, L.: An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data. Cent. Eur. J. Math. 11(8), 1489–1509 (2013). (In the Topical Issue Numerical Methods for Large Scale Scientific Computing)CrossRefMATHMathSciNet
16.
Pironneau, O.: Optimal Shape Design for Elliptic Systems. Springer-Verlag, Berlin (1984)
17.
Srivastava, P.K., Banerjee, M., Chandra, P.: Modeling the drug therapy for HIV infection. J. Biol. Syst. 17(2), 213–223 (2009)CrossRefMathSciNet
18.
Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-Posed Problems. Winston and Sons, Washington, DC (1977)MATH
19.
Tikhonov, A.N., Goncharsky, A.V., Stepanov, V.V., Yagola, A.G.: Numerical Methods for the Solution of Ill-Posed Problems. Kluwer, London (1995)CrossRefMATH
Metadata
Title
Time-adaptive FEM for distributed parameter identification in mathematical model of HIV infection with drug therapy
Authors
Larisa Beilina
Irina Gainova
Copyright Year
2015
Book
Inverse Problems and Applications

Print ISBN: 978-3-319-12498-8

Electronic ISBN: 978-3-319-12499-5

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-12499-5_8

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