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

Nikolay Koshev 1  and Larisa Beilina 2
  • 1 Department of Physics, Penza State University of Architecture and Building, German Titov 28, 440028, Penza, Russian Federation
  • 2 Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Maskingränd 2, 42196, Gothenburg, Sweden

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.

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