A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations
| Title: | A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations |
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| Authors: | da Veiga, Lourenço Beirão, Di Pietro, Daniele A., Droniou, Jérôme, Haile, Kirubell B., Radley, Thomas J. |
| Publication Year: | 2025 |
| Collection: | Computer Science Mathematics |
| Subject Terms: | Mathematics - Numerical Analysis, 65N30, 65N12, 35Q30, 76D07 |
| More Details: | 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. |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2502.15293 |
| Accession Number: | edsarx.2502.15293 |
| Database: | arXiv |
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