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

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Koshev N., Beilina L.

Open Mathematics

2013

tom 11

nr 8

1489-1509

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.

Ograniczanie wyników

1 Open Mathematics

1 Beilina L.

1 Koshev N.

1 2013

Wyniki wyszukiwania

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