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An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data

N. Koshev ; Larisa Beilina (Institutionen för matematiska vetenskaper, matematik)
Central European Journal of Mathematics (1895-1074). Vol. 11 (2013), 8, p. 1489-1509.
[Artikel, refereegranskad vetenskaplig]

We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally simulated and experimental backscattered data measured in microtomography.

Nyckelord: Fredholm integral equation of the first kind, Ill-posed problem, Adaptive finite element method, A posteriori error estimates, Tikhonov functional, Regularized solution



Denna post skapades 2013-06-27. Senast ändrad 2013-08-30.
CPL Pubid: 179332

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Geometri
Algebra och logik
Sannolikhetsteori och statistik

Chalmers infrastruktur