A Hybrid High-Order method for the steady incompressible Navier--Stokes problem - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Scientific Computing Année : 2018

A Hybrid High-Order method for the steady incompressible Navier--Stokes problem

Résumé

In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier--Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and is (relatively) inexpensive thanks to the possibility of statically condensing a subset of the unknowns at each nonlinear iteration. We show under general assumptions the existence of a discrete solution, which is also unique provided a data smallness condition is verified. Using a compactness argument, we prove convergence of the sequence of discrete solutions to minimal regularity exact solutions for general data. For more regular solutions, we prove optimal convergence rates for the energy-norm of the velocity and the $L^2$-norm of the pressure under a standard data smallness assumption. More precisely, when polynomials of degree $k\ge 0$ at mesh elements and faces are used, both quantities are proved to converge as $h^{k+1}$ (with $h$ denoting the meshsize).
Fichier principal
Vignette du fichier
nsho.pdf (492.82 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01349519 , version 1 (27-07-2016)
hal-01349519 , version 2 (13-01-2017)

Licence

Paternité

Identifiants

Citer

Daniele Di Pietro, Stella Krell. A Hybrid High-Order method for the steady incompressible Navier--Stokes problem. Journal of Scientific Computing, 2018, 74 (3), pp.1677-1705. ⟨10.1007/s10915-017-0512-x⟩. ⟨hal-01349519v2⟩
612 Consultations
313 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More