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

Nikolay Koshev ; Larisa Beilina

Open Mathematics, Tome 11 (2013), p. 1489-1509 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2013-01-01

Zbl 1312.65225

EUDML-ID : urn:eudml:doc:269552

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