A posteriori error estimators of gradient recovery type for FEM of a model optimal control problem (Q1872008)

The adaptive finite element method (FEM) is widely used in different fields of applied mathematics and plays a very important role in numerical solution of optimal control problems. In this paper a posteriori error estimators of gradient recovery type of the adaptive finite element method for a model optimal control problem of elliptic systems is derived. It is shown that the a posteriori error estimator is equivalent to the discrimination error in a norm of energy type on general meshes. When the solution of the optimal control problem is smooth and the meshes are uniform then the a posteriori estimators are asymptotically exact.