$L^2$ Norm Equivalent a Posteriori Error Estimate for a Constrained Optimal Control Problem

Abstract

Adaptive finite element approximation for a constrained optimal control problem is studied. A posteriori error estimators equivalent to the $L^2$ norm of the approximation error are derived both for the state and the control approximation, which are particularly suitable for an adaptive multi-mesh finite element scheme and applications where $L^2$ error is more important. The error estimators are then implemented and tested with promising numerical results.