Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2025

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

Résumé

In this paper we propose and analyze a new Finite Element method for the solution of the twoand 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.

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hal-05335706 , version 1 (28-10-2025)

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L Beirão da Veiga, Daniele A. Di Pietro, J Droniou, Kirubell B Haile, Thomas J Radley. A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier-Stokes equations. SIAM Journal on Numerical Analysis, 2025, 436, pp.117660. ⟨10.1016/j.cma.2024.117660⟩. ⟨hal-05335706⟩
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