A linearization technique and error estimates for distributed parameter identification in quasilinear problems

Abstract

The identification problem of a nonlinear functional coefficient in elliptic and parabolic quasilinear equations is considered. A distributed observation oi the solution of the corresponding equation is assumed to be known a priori. An identification method is introduced, which needs only a linear equation to be solved in each iteration step of the optimization. Estimates of the rate of convergence for the proposed approach are proved, when the equation is discretized with the finite element method with respect to space variables. Some numerical results are given.