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

Abstract

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 C¹ finite element method, and present the error analysis together with numerical results.

Keywords:

• Cubic Hermite element
• Dirichlet boundary condition
• elliptic distributed optimal control problem
• One dimensional
• pointwise derivative constraints

1991 MATHEMATICS SUBJECT CLASSIFICATION:

• 49J15
• 65N30
• 65N15

Additional information

Funding

The work of the first and second authors was supported in part by the US National Science Foundation under Grant No. DMS-19-13035.