This paper aims to improve guaranteed error control for the Stokes problem with a focus on pressure-robustness, i.e. for discretisations that compute a discrete velocity that is independent of the exact pressure. A Prager-Synge type result relates the velocity errors of divergence-free primal and perfectly equilibrated dual mixed methods for the velocity stress. The first main result of the paper is a framework with relaxed constraints on the primal and dual method. This enables to use a recently developed mass conserving mixed stress discretisation for the design of equilibrated fluxes and to obtain pressure-independent guaranteed upper bounds for any pressure-robust (not necessarily divergence-free) primal discretisation. The second main result is a provably efficient local design of the equilibrated fluxes with comparably low numerical costs. Numerical examples verify the theoretical findings and show that efficiency indices of our novel guaranteed upper bounds are close to one.

中文翻译：

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压力稳健斯托克斯离散化速度误差的保证上限

本文旨在改进 Stokes 问题的有保证的误差控制，重点是压力鲁棒性，即计算与精确压力无关的离散速度的离散化。Prager-Synge 类型的结果与速度应力的无散度原始和完全平衡双重混合方法的速度误差有关。本文的第一个主要结果是一个对原始方法和对偶方法具有宽松约束的框架。这使得能够使用最近开发的质量守恒混合应力离散化来设计平衡通量，并为任何压力稳健（不一定无散度）的原始离散化获得与压力无关的保证上限。第二个主要结果是平衡通量的可证明有效的局部设计，数值成本相对较低。