# Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale

• Volume: 33, Issue: 1, page 169-189
• ISSN: 0764-583X

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## Abstract

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The Navier–Stokes equations are approximated by means of a fractional step, Chorin–Temam projection method; the time derivative is approximated by a three-level backward finite difference, whereas the approximation in space is performed by a Galerkin technique. It is shown that the proposed scheme yields an error of $𝒪\left(\delta {t}^{2}+{h}^{l+1}\right)$ for the velocity in the norm of l2(L2(Ω)d), where l ≥ 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of projection schemes based on the incremental pressure correction is of $𝒪\left(\delta {t}^{2}\right)$ independent of the approximation order of the velocity time derivative.

## How to cite

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Guermond, Jean-Luc. "Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale." ESAIM: Mathematical Modelling and Numerical Analysis 33.1 (2010): 169-189. <http://eudml.org/doc/197451>.

@article{Guermond2010,
abstract = { The Navier–Stokes equations are approximated by means of a fractional step, Chorin–Temam projection method; the time derivative is approximated by a three-level backward finite difference, whereas the approximation in space is performed by a Galerkin technique. It is shown that the proposed scheme yields an error of $\{\cal O\}(\delta t^2 + h^\{l+1\})$ for the velocity in the norm of l2(L2(Ω)d), where l ≥ 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of projection schemes based on the incremental pressure correction is of $\{\cal O\}(\delta t^2)$ independent of the approximation order of the velocity time derivative. },
author = {Guermond, Jean-Luc},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = { Incompressible Navier–Stokes equations; Projection method; Second order approximation Fractional-step method; Finite elements. ; Incompressible Navier–Stokes equations; Projection method; Second order approximation Fractional-step method; Finite elements. ; error estimation; fractional step; Chorin-Temam projection method; three-level backward finite difference; Galerkin technique; splitting error},
language = {fre},
month = {3},
number = {1},
pages = {169-189},
publisher = {EDP Sciences},
title = {Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale},
url = {http://eudml.org/doc/197451},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Guermond, Jean-Luc
TI - Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 1
SP - 169
EP - 189
AB - The Navier–Stokes equations are approximated by means of a fractional step, Chorin–Temam projection method; the time derivative is approximated by a three-level backward finite difference, whereas the approximation in space is performed by a Galerkin technique. It is shown that the proposed scheme yields an error of ${\cal O}(\delta t^2 + h^{l+1})$ for the velocity in the norm of l2(L2(Ω)d), where l ≥ 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of projection schemes based on the incremental pressure correction is of ${\cal O}(\delta t^2)$ independent of the approximation order of the velocity time derivative.
LA - fre
KW - Incompressible Navier–Stokes equations; Projection method; Second order approximation Fractional-step method; Finite elements. ; Incompressible Navier–Stokes equations; Projection method; Second order approximation Fractional-step method; Finite elements. ; error estimation; fractional step; Chorin-Temam projection method; three-level backward finite difference; Galerkin technique; splitting error
UR - http://eudml.org/doc/197451
ER -

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