A One Dimensional Elliptic Distributed Optimal Control Problem with Pointwise Derivative Constraints

Susanne C. Brenner, Li-yeng Sung, Winnifried Wollner

Published 2020-03-18Version 1

We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain higher regularity for the optimal state under appropriate assumptions on the data. We also solve the optimal control problem as a fourth order variational inequality by a $C^1$ finite element method, and present the error analysis together with numerical results.