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October 7, 2025Open Access

A Posteriori Error Estimation for Pressure-Robust Finite Element Methods Applied to the Stokes Optimal Control Problem

Key Points

The proposed estimator effectively separates velocity and pressure errors, leading to more reliable estimates.
Numerical experiments validate that the a posteriori error estimator demonstrates global reliability and efficiency in applications.
This method is particularly applicable to the Stokes equations, enhancing performance in the associated optimal control problem.
The a posteriori error estimation methodology offers significant improvements over traditional methods by relying on a residual-based approach.

Abstract

This paper study a posteriori error estimates for the 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.

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