Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity. (19th December 2019)

• Record Type: Journal Article
• Authors: Jin, Bangti; Xu, Yifeng
• Is Part Of: Inverse problems. Volume 36:Number 1(2020)
• Publication Date: 2019-12-19
• Subjects: electrical impedance tomography -- piecewise constant conductivity -- a posteriori error estimator -- adaptive finite element method -- convergence analysis -- Modica–Mortola functional; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab261e
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this work we propose and analyze a numerical method for electrical impedance tomography to recover 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.