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

Nikolay Koshev, Larisa Beilina

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1489-1509
Number of pages21
JournalCentral European Journal of Mathematics
Volume11
Issue number8
DOIs
Publication statusPublished - Aug 2013
Externally publishedYes

Keywords

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

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