hp-Finite element discretisation of the electrical impedance tomography problem

This paper is concerned with the accurate recovery of the permittivity and conductivity from the solution of the electrical impedance tomography (EIT) inverse problem, given the knowledge of either the Neumann to Dirichlet or the Dirichlet to Neumann map. The linearised EIT inverse problem for the Fourier regime is discretised by hp-finite elements, which allows the accurate calculation of the sensitivity matrix entries. The variational algorithm of Knowles (1998) [31] is extended to allow the recovery of both material parameters by solution of the EIT problem in the Laplace regime. The associated forward problem is again discretised by hp-finite elements. A series of numerical results are included to demonstrate the effectiveness of the proposed techniques.