Adaptive Finite Element Approximation for an Elliptic Optimal Control Problem with Both Pointwise and Integral Control Constraints

• DOI: 10.1007/s10915-013-9790-0
• Publication Date: 2013-10-14T14:20:38Z
• Authors: Ning Du; Liang Ge; Wenbin Liu
• Keywords: 0101 mathematics; 01 natural sciences

In this paper, we study the adaptive finite element approximation for a constrained optimal control problem with both pointwise and integral control constraints. We first obtain the explicit solutions for the variational inequalities both in the continuous and discrete cases. Then a priori error estimates are established, and furthermore equivalent a posteriori error estimators are derived for both the state and the control approximation, which can be used to guide the mesh refinement for an adaptive multi-mesh finite element scheme. The a posteriori error estimators are implemented and tested with promising numerical results.