Abstract
We consider an adaptive finite element method for the solution of a Fredholm integral equation of the first kind and derive a posteriori error estimates both in the Tikhonov functional and in the regularized solution of this functional. We apply nonlinear results obtained in Beilina et al., (Journal of Mathematical Sciences, 167, 279–325, 2010), Beilina and Klibanov, (Inverse Problems, 26, 045012, 2010), Beilina et al., (Journal of Mathematical Sciences, 172, 449–476, 2011), Beilina and Klibanov, ( Inverse Problems, 26, 125009, 2010), Klibanov et al., (Inverse and Ill-Posed Problems), 19, 83–105, 2011) for the case of the linear bounded operator. We formulate an adaptive algorithm and present experimental verification of our adaptive technique on the backscattered data measured in microtomography.
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Acknowledgments
This research was supported by the Swedish Research Council, the Swedish Foundation for Strategic Research (SSF) in Gothenburg mathematical modelling centre (GMMC), and by the Swedish Institute, Visby Program. The first author acknowledges also the Russian Foundation For Basic Research, the grant RFFI 11-01-00040.
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Koshev, N., Beilina, L. (2013). A Posteriori Error Estimates for Fredholm Integral Equations of the First Kind. 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_5
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DOI: https://doi.org/10.1007/978-1-4614-7816-4_5
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