Identification of unknown diffusion coefficient in pure diffusive linear model of chronoamperometry. II. Numerical implementation

This article presents numerical implementation of the approach proposed in the previous study (Identification of the unknown diffusion coefficient in ion transport problem. I. The theory, Math. Chem. (2009) (submitted)) for the coefficient inverse problems related to linear diffusion equation in chronoamperometry. The coarse-fine grid algorithm is used for determination of the unknown diffusion coefficient D(x) in the linear parabolic equation u (t) = (D(x)u (x) ) (x) from the measured output data (left flux). The main distinguished feature of the implemented algorithm is the use of a fine grid for the numerical solution of well-posed forward and backward parabolic problems, and a coarse grid for the interpolation of the unknown diffusion coefficient D(x). The nodal values of the unknown coefficient on the coarse grid are recovered sequentially, solving on each step of the coarse grid iteration algorithm the well-posed forward, and the sequence of backward pababolic problems. This guarantees a compromise between the accuracy and stability of the solution of the considered inverse problem. An efficiency and applicability of the proposed approach is demonstrated on various numerical examples with noisy free and noisy data.