Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure

In this work we study the stability, convergence, and pressurerobustness 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 pressurerobustness. Several examples of existing and new schemes that fit into the framework are exhibited, and extensive numerical validation of the theoretical properties is provided.