Convergence of a numerical solver for an ℝ-linear Beltrami equation

Abstract

The convergence of the solution of the discretized R-linear Beltrami equation arising in a recent reconstruction algorithm for electrical impedance tomography based on the uniqueness proof of Astala-Päivärinta is investigated. A new discretization is introduced for the L p -convergence analysis and an O(h δ ) convergence result is proved given C δ -continuous coefficient functions. Numerical comparisons are made between three different methods. These suggest that the polar coordinate discretization method of Daripa applied in the present context is preferable.