Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929320676556800 |
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| author | Botti, Lorenzo Botti, Michele Di Pietro, Daniele Antonio Massa, Francesco Carlo |
| author_facet | Botti, Lorenzo Botti, Michele Di Pietro, Daniele Antonio Massa, Francesco Carlo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure Botti, Lorenzo Botti, Michele Di Pietro, Daniele Antonio Massa, Francesco Carlo Numerical Analysis 65N30, 65N12, 35Q30, 76D07 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. |
| title | Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure |
| topic | Numerical Analysis 65N30, 65N12, 35Q30, 76D07 |
| url | https://arxiv.org/abs/2404.12732 |