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Adaptive FEM for Electrical Impedance Tomography with a Piecewise Constant Conductivity

Jin, B; Xu, Y; (2019) Adaptive FEM for Electrical Impedance Tomography with a Piecewise Constant Conductivity. Inverse Problems , 36 (1) 10.1088/1361-6420/ab261e. Green open access

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Abstract

In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.

Type: Article
Title: Adaptive FEM for Electrical Impedance Tomography with a Piecewise Constant Conductivity
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/ab261e
Publisher version: https://doi.org/10.1088/1361-6420/ab261e
Language: English
Additional information: As the Version of Record of this article is going to be/has been published on a gold open access basis under a CC BY 3.0 licence, this Accepted Manuscript is available for reuse under a CC BY 3.0 licence immediately. Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permission may be required. All third party content is fully copyright protected, and is not published on a gold open access basis under a CC BY licence, unless that is specifically stated in the figure caption in the Version of Record.
Keywords: electrical impedance tomography, piecewise constant conductivity, Modica-Mortola functional, a posteriori error estimator, adaptive finite element method, convergence analysis
UCL classification: UCL
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/10073392
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