  In this paper we investigate the problem of identifying conductivity in
electrical impedance tomography from one boundary measurement. A variational
method with total variation regularization is here proposed to tackle this
problem. We discretize the PDE as well as the conductivity with piecewise
linear, continuous finite elements. We prove the stability and convergence of
this technique. For the numerical solution we propose a projected Armijo
algorithm. Finally, a numerical experiment is presented to illustrate our
theoretical results.
