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arXiv · 2502.16482

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

Jingshi Li·Jiachuan Zhang
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Abstract

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.

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Jingshi Li, Jiachuan Zhang. 2025-02-23. A Posteriori Error Estimation Improved by a Reconstruction Operator for the Stokes Optimal Control Problem. https://arxiv.org/abs/2502.16482

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