A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915688987230208 |
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| author | da Veiga, Lourenço Beirão Di Pietro, Daniele A. Droniou, Jérôme Haile, Kirubell B. Radley, Thomas J. |
| author_facet | da Veiga, Lourenço Beirão Di Pietro, Daniele A. Droniou, Jérôme Haile, Kirubell B. Radley, Thomas J. |
| contents | In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The proposed method is pressure-robust, i.e., irrotational forcing terms do not affect the approximation of the velocity, and Reynolds-quasi-robust, with error estimates that, for smooth enough exact solutions, do not depend on the inverse of the viscosity. We carry out an in-depth convergence analysis highlighting pre-asymptotic convergence rates and validate the theoretical findings with a complete set of numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations da Veiga, Lourenço Beirão Di Pietro, Daniele A. Droniou, Jérôme Haile, Kirubell B. Radley, Thomas J. Numerical Analysis 65N30, 65N12, 35Q30, 76D07 In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The proposed method is pressure-robust, i.e., irrotational forcing terms do not affect the approximation of the velocity, and Reynolds-quasi-robust, with error estimates that, for smooth enough exact solutions, do not depend on the inverse of the viscosity. We carry out an in-depth convergence analysis highlighting pre-asymptotic convergence rates and validate the theoretical findings with a complete set of numerical experiments. |
| title | A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations |
| topic | Numerical Analysis 65N30, 65N12, 35Q30, 76D07 |
| url | https://arxiv.org/abs/2502.15293 |