A Posteriori Error Estimation Improved by a Reconstruction Operator for the Stokes Optimal Control Problem

This paper focuses on a posteriori error estimates for a pressure‐robust finite element method, which incorporates a divergence‐free reconstruction operator, within the context of the distributed optimal control problem constrained by the Stokes equations. We develop an enhanced residual‐based a posteriori error estimator that is independent of pressure and establish its global reliability and efficiency. The proposed a posteriori error estimator enables the separation of velocity and pressure errors in a posteriori error estimation, ensuring velocity‐related estimates are free of pressure influence. Numerical experiments confirm our conclusions.