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.

翻译：本文旨在改进斯托克斯问题的保证误差控制, 重点是压力- 气压分解, 即用于分解, 计算离散速度, 且不取决于确切压力。 一个 Prager- Synge 类型的结果将无偏差的原始和完全均匀的双向混合方法的速度差对速度压力压力压力压力压力。 本文的第一个主要结果是一个框架, 对原始和双向方法有宽松的限制。 这使得能够使用最近开发的大规模保护混合压力分解来设计平衡通量, 并获得任何压力- 气压- 气压( 不一定无偏差) 原始分解所需的依赖压力- 保证上界。 第二个主要结果是以可比较的低数字成本对均衡通量的通量进行精巧的本地设计。 数字实例可以证实理论结论, 并显示我们新的保证上界的效率指数接近于一个。