Abstract
In this work, we extend our previous work (Li and Wang, 2023) of the discontinuous Galerkin (DG) method for Electrical Impedance Tomography (EIT) with full data to partial data where the current and voltage measurements are taken only on part of the boundary. Additionally, we provide the convergence analysis of the DG approximation for EIT for partial data based on an iterative method with Tikhonov regularization. We prove that the minimizers of the discrete optimization problems converge to a minimizer of the continuous optimization problem as the mesh sizes of the discretization approach zero. Numerical results for the recovery of conductivities are tested with different types of partial data. The partial data results are demonstrated to be comparable to the full data results.
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