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.
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science
Cited by
4 articles.
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