In this paper we investigate the problem of identifying conductivity inelectrical impedance tomography from one boundary measurement. A variationalmethod with total variation regularization is here proposed to tackle thisproblem. We discretize the PDE as well as the conductivity with piecewiselinear, continuous finite elements. We prove the stability and convergence ofthis technique. For the numerical solution we propose a projected Armijoalgorithm. Finally, a numerical experiment is presented to illustrate ourtheoretical results.
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