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An adaptive finite ...
An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data
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- Koshev, N. (författare)
- Penza State University of Architecture and Construction
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- Beilina, Larisa, 1970 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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(creator_code:org_t)
- Walter de Gruyter GmbH, 2013
- 2013
- Engelska.
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Ingår i: Central European Journal of Mathematics. - : Walter de Gruyter GmbH. - 1895-1074 .- 1644-3616. ; 11:8, s. 1489-1509
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
Nyckelord
- Fredholm integral equation of the first kind
- Ill-posed problem
- Adaptive finite element method
- A posteriori error estimates
- Tikhonov functional
- Regularized solution
- Adaptive finite element method
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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