# A Convergent Adaptive Finite Element Method for Electrical Impedance Tomography

arXiv: https://arxiv.org/abs/1608.03170 · HTML: https://mlsanity.com/paper/1608.03170/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2016.

## Built on by (most cited first, 2 of 2)

- [Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches](https://mlsanity.com/paper/2310.18636/) (2023)
- [Multi-Scale Frequency-Enhanced Deep D-bar Method for Electrical Impedance Tomography](https://mlsanity.com/paper/2407.03335/) (2024)

## Abstract (arXiv)

In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for 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.