| Title: |
A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations |
| 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 |
