Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure
<|reference_start|>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 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.<|reference_end|>
@article{botti2024stability,,
    title={Stability, convergence, and pressure-robustness of numerical schemes for
  incompressible flows with hybrid velocity and pressure},
    author={Lorenzo Botti, Michele Botti, Daniele Antonio Di Pietro and Francesco
  Carlo Massa},
    journal={arXiv preprint arXiv:2404.12732},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.12732},
    primaryClass={math.NA cs.NA}
}