In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions that yield inf-sup stability as well as error estimates which distinguish the velocity- and pressure-related contributions to the error. We additionally identify the key properties under which the pressure-related contributions vanish in the estimate of the velocity, thus leading to pressure-robustness. Several examples of existing and new schemes that fit into the framework are provided, and extensive numerical validation of the theoretical properties is provided.

翻译：本文研究混合速度和压力离散方法在不可压缩流中的稳定性、收敛性及压力鲁棒性。具体聚焦于Stokes问题，我们提出一组假设条件，这些条件既能保证inf-sup稳定性，又能得到区分速度与压力相关误差贡献的误差估计。此外，我们确定了使速度估计中压力相关贡献消失的关键性质，从而实现压力鲁棒性。文中给出了多个符合该框架的现有及新格式示例，并通过广泛数值实验验证了理论性质。