Guaranteed upper bounds for the velocity error of pressure-robust Stokes discretisations

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