# 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 (2013)

- Volume: 11, Issue: 8, page 1489-1509
- ISSN: 2391-5455

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topNikolay Koshev, and Larisa Beilina. "An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data." Open Mathematics 11.8 (2013): 1489-1509. <http://eudml.org/doc/269552>.

@article{NikolayKoshev2013,

abstract = {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.},

author = {Nikolay Koshev, Larisa Beilina},

journal = {Open Mathematics},

keywords = {Fredholm integral equation of the first kind; Ill-posed problem; Adaptive finite element method; A posteriori error estimates; Tikhonov functional; Regularized solution; ill-posed problem; adaptive finite element method; a posteriori error estimates; Tikhonov regularization; a posteriori error estimator; numerical experiment},

language = {eng},

number = {8},

pages = {1489-1509},

title = {An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data},

url = {http://eudml.org/doc/269552},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Nikolay Koshev

AU - Larisa Beilina

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

JO - Open Mathematics

PY - 2013

VL - 11

IS - 8

SP - 1489

EP - 1509

AB - 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.

LA - eng

KW - Fredholm integral equation of the first kind; Ill-posed problem; Adaptive finite element method; A posteriori error estimates; Tikhonov functional; Regularized solution; ill-posed problem; adaptive finite element method; a posteriori error estimates; Tikhonov regularization; a posteriori error estimator; numerical experiment

UR - http://eudml.org/doc/269552

ER -

## References

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