Improved Crouzeix-Raviart scheme for the Stokes and Navier-Stokes problem

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: H 1 (Ω)∩ H (div 0; Ω) := {v ∈ H 1 (Ω) : div v = 0}. The non-conforming Crouzeix-Raviart finite element are convenient since they induce local mass conser...

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Bibliographic Details
Published in:	ESAIM. Proceedings and surveys Vol. 76; pp. 20 - 34
Main Authors:	Chénier, Eric, Jamelot, Erell, Le Potier, Christophe, Peitavy, Andrew
Format:	Journal Article
Language:	English
Published:	Les Ulis EDP Sciences 2024
Subjects:	Approximation Finite element analysis Fluid flow Navier-Stokes equations
Online Access:	Get full text
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Summary:	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: H 1 (Ω)∩ H (div 0; Ω) := {v ∈ H 1 (Ω) : div v = 0}. 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).
ISSN:	2267-3059 2267-3059
DOI:	10.1051/proc/202476020