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A convergent adaptive finite element method for electrical impedance tomography

Jin, B; Xu, Y; Zou, J; (2017) A convergent adaptive finite element method for electrical impedance tomography. IMA Journal of Numerical Analysis , 37 (3) pp. 1520-1550. 10.1093/imanum/drw045. Green open access

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Abstract

In this work, we develop and analyse an adaptive finite element method for efficiently solving electrical impedance tomography—a severely ill-posed nonlinear inverse problem of recovering the conductivity from boundary voltage measurements. The reconstruction technique is based on Tikhonov regularization with a Sobolev smoothness penalty and discretizing the forward model using continuous piecewise linear finite elements. We derive an adaptive finite element algorithm with an a posteriori error estimator involving the concerned state and adjoint variables and the recovered conductivity. The convergence of the algorithm is established, in the sense that the sequence of discrete solutions contains a convergent subsequence to a solution of the optimality system for the continuous formulation. Numerical results are presented to verify the convergence and efficiency of the algorithm.

Type: Article
Title: A convergent adaptive finite element method for electrical impedance tomography
Open access status: An open access version is available from UCL Discovery
DOI: 10.1093/imanum/drw045
Publisher version: https://doi.org/10.1093/imanum/drw045
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: electrical impedance tomography, a posteriori error estimator, adaptive finite element method, convergence analysis
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10052336
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