In order to obtain regularized approximations for the solution q of the parameter identification problem -∇.(q∇u) = f in Ω along with the Neumann boundary condition q ∂u/∂v = g on ∂Ω, which is an ill-posed problem, we consider its weak formulation as a linear operator equation with operator as a function of the data u ∈ W1,∞(Ω), and then apply the Tikhonov regularization and a finite-dimensional approximation procedurewhen the data is noisy. Here, Ω is a bounded domain inRd with Lipschitz boundary, f ∈ L2(Ω) and g ∈ H-1/2(∂ Ω). This approach is akin to the equation error method of Al-Jamal and Gockenback (2012) wherein error estimates are obtained in terms of a quotient norm, whereas our procedure facilitates to obtain error estimates in terms of the regularization parameters and data errors with respect to the norms of the spaces under consideration. In order to obtain error estimates when the noisy data belongs to L2(Ω) instead of W1,∞(Ω), we shall make use of a smoothing procedure using the Clement operator under additional assumptions of Ω and u. © 2017 Walter de Gruyter GmbH, Berlin/Boston.