Applications of the duality theory of convex analysis to the complete electrode model of electrical impedance tomography (Selecciones Matemáticas, 2023)
The duality theory of convex analysis is applied to the complete electrode model (CEM), which is a standard model in electrical impedance tomography (EIT). This results in a dual formulation of the CEM and a general error estimate. This new formulation of the CEM is written in terms of current fields and is shown to have a unique solution. Using this formulation, the general error estimate is proved, from which two a posteriori error estimates and a well known asymptotic result on CEM solutions are obtained. The first a posteriori error estimate assesses the accuracy of solutions to approximate problems, and the second one assesses the accuracy of approximate solutions. Numerical tests to apply this second estimate are performed, employing the finite element method to obtain approximate solutions.