In this paper the regularization method applied to the numerical identification of the diffusion coefficient in second order elliptic equations is investigated. For solving the corresponding regularized discrete and continuous nonlinear minimization problems the Gauss-Newton method is analyzed. We describe an effective way for performing one iteration step which requires to solve one problem of 2nd order and one problem of 4th order.
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Volkmar Friedrich, Ulrich Tautenhahn, Regularized Parameter Identification in Elliptic Boundary Value Problems. Z. Anal. Anwend. 8 (1989), no. 1, pp. 3–11DOI 10.4171/ZAA/332