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

2025/02/23 by Jingshi Li, Li, Jingshi, Jiachuan Zhang +1
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2502.16482

openalex publication_date 2025/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

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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