M. Hanke et O. Scherzer, Error analysis of an equation error method for the identification of the diffusion coefficient in a quasi-linear parabolic differential equation, SIAM J A MA, 59(3), 1999, pp. 1012-1027
We consider the inverse problem of reconstructing the diffusion coefficient
in a quasi-linear parabolic differential equation in divergence form from
measurements of the solution at a finite number of points in the interior o
f the domain. An equation error method is developed which transforms the in
verse problem into a system of linear operator equations for the diffusion
coefficient and which can be solved by the conjugate gradient method in a v
ery efficient and stable manner. A detailed error analysis relates the requ
ired number of measurements with their accuracy. Numerical results illustra
te the performance of the method.