In this contribution the identification of a piecewise linear diffusion function in a nonlinear convection-diffusion equation is presented. This inverse problem arises at the parameter identification for a sedimentation-consolidation process of flocculated suspensions in a batch settling experiment. The identification method avoids the minimization of a cost function with the method of least squares. Instead, in each computational time step of the finite difference scheme, the unknown diffusion function is extended by appending a new linear interval to the piecewise linear polygon. The required information is exclusively obtained from an overspecified boundary condition and by employing the discrete solution of the finite difference scheme for the direct problem. The advantage of the proposed approach is its low computational cost.