Adaptive optimal control approximation for solving a fourth-order elliptic variational inequality

An optimal control approach is proposed to solve the fourth-order elliptic variational inequality with curvature obstacle. It is proved that the variational inequality is equivalent to the constrained optimal control problem. The finite element approximation of the optimal control problem is constructed and the a priori error estimates and the equivalent a posteriori error estimators are derived. Some numerical experiments are performed to confirm a priori error estimates and demonstrate the effectiveness of the a posteriori estimators.