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

Botti, Lorenzo; Botti, Michele; Di Pietro, Daniele; Massa, Francesco

doi:10.1090/mcom/4049

Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure
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by Lorenzo Botti, Michele Botti, Daniele A. Di Pietro and Francesco Carlo Massa;

Math. Comp.

DOI: https://doi.org/10.1090/mcom/4049

Published electronically: January 22, 2025

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Abstract:

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 exhibited, and extensive numerical validation of the theoretical properties is provided.

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