TY  - JOUR
KW  - electrical impedance tomography
KW  -  a posteriori error estimator
KW  -  adaptive finite element method
KW  -  convergence analysis
IS  - 3
AV  - public
JF  - IMA Journal of Numerical Analysis
SN  - 0272-4979
SP  - 1520
ID  - discovery10052336
A1  - Jin, B
A1  - Xu, Y
A1  - Zou, J
UR  - https://doi.org/10.1093/imanum/drw045
VL  - 37
N2  - 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.
EP  - 1550
TI  - A convergent adaptive finite element method for electrical impedance tomography
Y1  - 2017/07//
N1  - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions.
PB  - OXFORD UNIV PRESS
ER  -