Gradient method with AFEM for parameter-estimation

We consider the adaptive finite element discretization of parameter estimation problems for nonlinear elliptic partial differential equations. The idea is to use a gradient method on finite-dimensional space minimization least-squares residual. Since involves solution equations, it not accesable, and replaced by an approximation obtained elements. This results into perturbed method. (a posteriori) error estimator control accuracy propose algorithm, which links progress iteration. show convergence algorithm under typical structural assumptions.