The most realistic model for current-to-voltage measurements of electrical impedance tomography is the complete electrode model which takes into account electrode shapes and contact impedances at the electrode/object interfaces. When contact impedances are small, numerical instability can be avoided by replacing the complete model with the shunt model in which perfect contacts, that is zero contact impedances, are assumed. In the present work we show that using the shunt model causes only a (almost) linear error with respect to the contact impedances in modelling absolute current-to-voltage measurements. Moreover, we note that the electric potentials predicted by the two models exhibit different Sobolev regularity properties. This causes, in particular, different convergence rates for a widely used finite element approximation of the potentials. The theoretical results are backed up by two-dimensional numerical experiments.
DOI: 10.1051/m2an/2015049
Keywords: Electric impedance tomography, complete electrode model, shunt model, mixed boundary conditions, elliptic boundary value problems
@article{M2AN_2016__50_2_415_0, author = {Dard\'e, J\'er\'emi and Staboulis, Stratos}, title = {Electrode modelling: {The} effect of contact impedance}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {415--431}, publisher = {EDP-Sciences}, volume = {50}, number = {2}, year = {2016}, doi = {10.1051/m2an/2015049}, mrnumber = {3482549}, zbl = {1339.35304}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015049/} }
TY - JOUR AU - Dardé, Jérémi AU - Staboulis, Stratos TI - Electrode modelling: The effect of contact impedance JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 415 EP - 431 VL - 50 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015049/ DO - 10.1051/m2an/2015049 LA - en ID - M2AN_2016__50_2_415_0 ER -
%0 Journal Article %A Dardé, Jérémi %A Staboulis, Stratos %T Electrode modelling: The effect of contact impedance %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 415-431 %V 50 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015049/ %R 10.1051/m2an/2015049 %G en %F M2AN_2016__50_2_415_0
Dardé, Jérémi; Staboulis, Stratos. Electrode modelling: The effect of contact impedance. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 2, pp. 415-431. doi : 10.1051/m2an/2015049. http://www.numdam.org/articles/10.1051/m2an/2015049/
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