论文标题
保证的上限，用于压力射击的速度误差stokes离散
Guaranteed upper bounds for the velocity error of pressure-robust Stokes discretisations
论文作者
论文摘要
本文旨在改善对Stokes问题的保证误差控制，重点放在压力稳定性上，即计算计算独立于确切压力的离散速度的离散性。 Prager-同步类型的结果将无差异原始和完全平衡的双重混合方法的速度误差与速度应力的速度误差有关。本文的第一个主要结果是对原始方法和双重方法的限制放松的框架。这使得可以使用最近开发的质量保存混合应力离散化来设计平衡通量，并为任何压力稳定（不一定是无差异）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，事实证明，平衡通量的局部设计具有相当低的数值成本。数值示例验证了理论发现，并表明我们新颖的保证上限的效率指数接近一个。
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.
