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.
@article{arxiv.2502.16482,
title = {A Posteriori Error Estimation Improved by a Reconstruction Operator for the Stokes Optimal Control Problem},
author = {Jingshi Li and Jiachuan Zhang},
journal= {arXiv preprint arXiv:2502.16482},
year = {2026}
}