  This work reformulates the complete electrode model of electrical impedance
tomography in order to enable more efficient numerical solution. The model
traditionally assumes constant contact conductances on all electrodes, which
leads to a discontinuous Robin boundary condition since the gaps between the
electrodes can be described by vanishing conductance. As a consequence, the
regularity of the electromagnetic potential is limited to less than two
square-integrable weak derivatives, which negatively affects the convergence
of, e.g., the finite element method. In this paper, a smoothened model for the
boundary conductance is proposed, and the unique solvability and improved
regularity of the ensuing boundary value problem are proven. Numerical
experiments demonstrate that the proposed model is both computationally
feasible and also compatible with real-world measurements. In particular, the
new model allows faster convergence of the finite element method.
