Error Analysis of an Equation Error Method for the Identification of the Diffusion Coefficient in a Quasi-linear Parabolic Differential Equation

We consider the inverse problem of reconstructing the diiusion coeecient in a quasilinear parabolic diierential equation in divergence form from measurements of the solution at a nite number of points in the interior of the domain. An equation error method is developed which transforms the inverse problem into a system of linear operator equations for the diiusion coeecient, and which can be solved by the conjugate gradient method in a very eecient and stable manner. A detailed error analysis relates the required number of measurements with their accuracy. Numerical results illustrate the performance of the method.