# 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 (2010)

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

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topGuermond, 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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