Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise Control and State Constraints

Abstract:    In this talk, we study conforming and nonconforming finite element methods for elliptic distributed optimal control problems with pointwise state and control constraints. The state control constrained minimization problem is solved for the state variable by reducing it into a fourth order variational inequality and convergence of the state error is established in the H2-like energy norm. The key ingredients are constraint preserving properties of the interpolation operator and the enriching map. We also discuss post-processing methods to obtain the approximation of the control from the discrete state. Finally, we present numerical results to illustrate theoretical findings.