ABSTRACT
In the parameter estimation problem governed by the partial differential equations, the finite element approximation plays a very important role (see, for examples, [2] and [12]). It is to be expected that the efficiency of the numerical methods will be influenced by the discretization scheme. The adaptive finite element method is the most important mean to boost the reliability and efficiency of the finite element discretization. The key is to find an a posteriori error estimator that is used to guide the mesh refinement. Roughly speaking, there are residual-type error estimators and recovery-type error estimators. For the literature, readers are referred to recent books by Ainsworth-Oden [1], an earlier book by Verfu¨rth [20], and the references cited therein.
