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In this work, we develop an efficient high order discontinuous Galerkin (DG)method for solving the Electrical Impedance Tomography (EIT). EIT is a highlynonlinear ill-posed inverse problem where the interior conductivity of anobject is recovered from the surface measurements of voltage and current flux.We first propose a new optimization problem based on the recovery of theconductivity from the Dirichlet-to-Neumann map to minimize the mismatch betweenthe predicted current and the measured current on the boundary. And we furtherprove the existence of the minimizer. Numerically the optimization problem issolved by a third order DG method with quadratic polynomials. Numerical resultsfor several two-dimensional problems with both single and multiple inclusionsare demonstrated to show the high {accuracy and efficiency} of the proposedhigh order DG method. Analysis and computation for discontinuous conductivitiesare also studied in this work.

A high order discontinuous Galerkin method for the recovery of the conductivity in Electrical Impedance Tomography