ELECTRODE MODELLING: THE EFFECT OF CONTACT IMPEDANCE

Abstract. Current-to-voltage measurements of electrical impedance tomography are accurately modelled by the complete electrode model which takes into account the contact impedance at the electrode/object interface. The formal limiting case is the shunt model, in which perfect contacts, that is, vanishing contact impedance is assumed. The main objective of this work is to study the relationship between these two models. In smooth geometry, we show that the energy norm discrepancy is almost of order square root of the contact impedance. In addition to this, we consider the discrepancy between the finite dimensional electrode potentials which are used as forward models in many practical applications: interpreting the shunt model as an orthogonal projection of the complete electrode model and applying a duality argument implies that this discrepancy decays twice as fast. We also demonstrate that in the limit, part of the Sobolev regularity of the spatial potential is lost; this possibly has the undesirable effect of slowing down the convergence of its numerical approximation. The theoretical results are backed up by two dimensional numerical experiments: one probing the asymptotic relationship between the models and another one testing the effect of the contact impedance on the finite element approximation of the complete electrode model. 1. Introduction. Th