  We consider Inverse Electrical Impedance Tomography (EIT) problem on
recovering electrical conductivity and potential in the body based on the
measurement of the boundary voltages on the $m$ electrodes for a given
electrode current. The variational formulation is pursued in the optimal
control framework, where electrical conductivity and boundary voltages are
control parameters, and the cost functional is the norm declinations of the
boundary electrode current from the given current pattern and boundary
electrode voltages from the measurements. EIT optimal control problem is fully
discretized using the method of finite differences. New Sobolev-Hilbert space
is introduced, and the convergence of the sequence of finite-dimensional
optimal control problems to EIT coefficient optimal control problem is proved
both with respect to functional and control in 2- and 3-dimensional domains.
