Improved Crouzeix-Raviart scheme for the Stokes and Navier-Stokes problem
ESAIM. Proceedings, Tome 76 (2024), pp. 20-34
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The resolution of the incompressible Navier-Stokes equations is tricky, and it is well known that one of the major issue is to approach the space: H1(Ω)∩ H(div 0; Ω) := {v ∈ H1(Ω) : div v = 0}. H 1 (Ω)∩ H ( div 0 ;Ω):= { v ∈ H 1 (Ω): div v = 0 }. $$ \mathbf{H}^1(\Omega) \cap \mathbf{H}(\operatorname{div} 0 ; \Omega):=\left\{\mathbf{v} \in \mathbf{H}^1(\Omega): \operatorname{div} \mathbf{v}=0\right\}. $$ The non-conforming Crouzeix-Raviart finite element are convenient since they induce local mass conservation. Moreover they are such that the stability constant of the Fortin operator is equal to 1. This implies that they can easily handle anisotropic mesh. However spurious velocities may appear and damage the approximation.We propose a scheme here that allows one to reduce the spurious velocities. It is based on a new discretisation for the gradient of pressure based on the symmetric MPFA scheme (finite volume MultiPoint Flux Approximation).
Affiliations des auteurs :
Eric Chénier 1 ; Erell Jamelot 2 ; Christophe Le Potier 2 ; Andrew Peitavy 2
@article{EP_2024_76_a2,
author = {Eric Ch\'enier and Erell Jamelot and Christophe Le Potier and Andrew Peitavy},
title = {Improved {Crouzeix-Raviart} scheme for the {Stokes} and {Navier-Stokes} problem},
journal = {ESAIM. Proceedings},
pages = {20--34},
year = {2024},
volume = {76},
doi = {10.1051/proc/202476020},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202476020/}
}
TY - JOUR AU - Eric Chénier AU - Erell Jamelot AU - Christophe Le Potier AU - Andrew Peitavy TI - Improved Crouzeix-Raviart scheme for the Stokes and Navier-Stokes problem JO - ESAIM. Proceedings PY - 2024 SP - 20 EP - 34 VL - 76 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202476020/ DO - 10.1051/proc/202476020 LA - en ID - EP_2024_76_a2 ER -
%0 Journal Article %A Eric Chénier %A Erell Jamelot %A Christophe Le Potier %A Andrew Peitavy %T Improved Crouzeix-Raviart scheme for the Stokes and Navier-Stokes problem %J ESAIM. Proceedings %D 2024 %P 20-34 %V 76 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202476020/ %R 10.1051/proc/202476020 %G en %F EP_2024_76_a2
Eric Chénier; Erell Jamelot; Christophe Le Potier; Andrew Peitavy. Improved Crouzeix-Raviart scheme for the Stokes and Navier-Stokes problem. ESAIM. Proceedings, Tome 76 (2024), pp. 20-34. doi: 10.1051/proc/202476020
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