A Posteriori Error Estimates for Fredholm Integral Equations of the First Kind

N. Koshev, L. Beilina

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Citations (Scopus)

Abstract

We consider an adaptive finite element method for the solution of a Fredholm integral equation of the first kind and derive a posteriori error estimates both in the Tikhonov functional and in the regularized solution of this functional. We apply nonlinear results obtained in Beilina et al., (Journal of Mathematical Sciences, 167, 279-325, 2010), Beilina and Klibanov, (Inverse Problems, 26, 045012, 2010), Beilina et al., (Journal of Mathematical Sciences, 172, 449-476, 2011), Beilina and Klibanov, (Inverse Problems, 26, 125009, 2010), Klibanov et al., (Inverse and Ill-Posed Problems), 19, 83-105, 2011) for the case of the linear bounded operator. We formulate an adaptive algorithm and present experimental verification of our adaptive technique on the backscattered data measured in microtomography.

Original languageEnglish
Title of host publicationApplied Inverse Problems - Select Contributions from the First Annual Workshop on Inverse Problems
Pages75-93
Number of pages19
DOIs
Publication statusPublished - 2013
Externally publishedYes
Event1st Annual Workshop on Inverse Problems - Gothenburg, Sweden
Duration: 2 Jun 20113 Jun 2011

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume48
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference1st Annual Workshop on Inverse Problems
Country/TerritorySweden
CityGothenburg
Period2/06/113/06/11

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