Adaptive finite element method for optimal control problems

In this paper, we provide the finite element method with multi-set adaptive meshes and multi-set base functions in developing efficient algorithms for constrained optimal control problems. We derive equivalent a posteriori error estimators of recovery type for both the state and the control approximation, which particularly suit a multi-set adaptive finite element scheme. We then propose a simple and yet efficient adaptive finite element algorithm, which is able to solve constrained control problems efficiently. Numerical results demonstrating our theoretical results are also presented in this paper.