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

• Autorzy: Nikolay Koshev , Larisa Beilina
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 65R32: Inverse problems
• 65R20: Integral equations
• 65R30: Improperly posed problems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 8
• Strony: 1489-1509

Daty

wydano

2013-08-01

online

2013-05-22

Twórcy

autor

Nikolay Koshev

• Penza State University of Architecture and Building

autor

Larisa Beilina

• Chalmers University of Technology and University of Gothenburg

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0247-3