An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data
Journal article, 2013

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.

Regularized solution

A posteriori error estimates

Ill-posed problem

Adaptive finite element method

Tikhonov functional

Fredholm integral equation of the first kind

Author

N. Koshev

Penza State University of Architecture and Construction

Larisa Beilina

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Central European Journal of Mathematics

1895-1074 (ISSN) 1644-3616 (eISSN)

Vol. 11 8 1489-1509

Subject Categories

Algebra and Logic

Geometry

Probability Theory and Statistics

DOI

10.2478/s11533-013-0247-3

More information

Created

10/6/2017