Convergence error exploration for electrical impedance tomography problems with open and closed domains

A fundamental part of the design of electrical impedance tomography (EIT) experiments is the selection of the structure of the computational mesh. Individual mesh elements are required to be sufficiently small to recover the behavior stated on the partial differential equations (PDE) EIT model. On the contrary, mesh elements needs to be not so small to fit the computation constraints of modern hardware. The target is to allow a fast iterative execution of the PDE model as performed by many optimization schemes. The estimation of the error over a reference mesh size is an important factor to compare with the total computation time for mesh generation, forward model evaluation, and tomographic inversion. In this work, we analyze the a posteriori convergence of EIT image reconstruction algorithms with respect to the mesh element size and computation time for open and closed domains. The tomographic inversion error is estimated using Euclidean and Jaccard distances for the output images.