Comptes Rendus
no. 6
Mathematical Problems in Mechanics/Numerical Analysis
Sharp error estimates for a fractional-step method applied to the 3D Navier–Stokes equations
[Estimations optimales d'erreur d'une méthode de pas fractionnaire appliqué à des équations de Navier–Stokes 3D]

Présenté par : Philippe G. Ciarlet

Francisco Guillén-González1 ; María Victoria Redondo-Neble2
1 Depto. EDAN, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
2 Depto. de Matemáticas, Universidad de Cádiz, C.A.S.E.M. Polígono Río San Pedro S/N, 11510 Puerto Real, Cádiz, Spain
Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 359-362.

On présente quelques améliorations sur les estimations d'erreur obtenues par J. Blasco et R. Codina pour une discrétisation des équations de Navier–Stokes par un schéma de décomposition en temps et des éléments finis en espace. L'idée principale est l'obtention de nouvelles estimations d'erreur de la dérivée discrète en temps de la vitesse, qui entraînent des estimations d'erreur d'ordre un (en temps et en espace) pour l'approximation de la pression.

We present some improvements on the error estimates obtained by J. Blasco and R. Codina for a viscosity-splitting in time scheme, with finite element approximation, applied to the Navier–Stokes equations. The key is to obtain new error estimates for the discrete in time derivative of velocity, which let us reach, in particular, an error of order one (in time and space) for the pressure approximation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.07.007

Francisco Guillén-González 1 ; María Victoria Redondo-Neble 2

1 Depto. EDAN, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
2 Depto. de Matemáticas, Universidad de Cádiz, C.A.S.E.M. Polígono Río San Pedro S/N, 11510 Puerto Real, Cádiz, Spain 
@article{CRMATH_2007__345_6_359_0,
     author = {Francisco Guill\'en-Gonz\'alez and Mar{\'\i}a Victoria Redondo-Neble},
     title = {Sharp error estimates for a fractional-step method applied to the {3D} {Navier{\textendash}Stokes} equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {359--362},
     publisher = {Elsevier},
     volume = {345},
     number = {6},
     year = {2007},
     doi = {10.1016/j.crma.2007.07.007},
     language = {en},
}
TY  - JOUR
AU  - Francisco Guillén-González
AU  - María Victoria Redondo-Neble
TI  - Sharp error estimates for a fractional-step method applied to the 3D Navier–Stokes equations
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 359
EP  - 362
VL  - 345
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2007.07.007
LA  - en
ID  - CRMATH_2007__345_6_359_0
ER  - 
%0 Journal Article
%A Francisco Guillén-González
%A María Victoria Redondo-Neble
%T Sharp error estimates for a fractional-step method applied to the 3D Navier–Stokes equations
%J Comptes Rendus. Mathématique
%D 2007
%P 359-362
%V 345
%N 6
%I Elsevier
%R 10.1016/j.crma.2007.07.007
%G en
%F CRMATH_2007__345_6_359_0
Francisco Guillén-González; María Victoria Redondo-Neble. Sharp error estimates for a fractional-step method applied to the 3D Navier–Stokes equations. Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 359-362. doi : 10.1016/j.crma.2007.07.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.007/

[1] J. Blasco, Thesis, UPC, Barcelona, Spain, 1996

[2] J. Blasco; R. Codina Error estimates for a viscosity-splitting, finite element method for the incompressible Navier–Stokes equations, Appl. Numer. Math., Volume 51 (2004), pp. 1-17

[3] J. Blasco, R Codina, Estimaciones de error para un método de paso fraccionado en elementos finitos para la ecuación de Navier–Stokes incompresible, in: Proocedings (in CD-ROM) of congress XVII C.E.D.Y.A. /VII C.M.A., 2001

[4] J.L. Guermond; L. Quartapelle On the approximation of the unsteady Navier–Stokes equations by finite elements projection methods, Numer. Math., Volume 80 (1998), pp. 207-238

[5] F. Guillén-González, M.V. Redondo-Neble, New error estimates for a viscosity-splitting scheme for the 3D Navier–Stokes equations, submitted for publication

[6] J. Shen On error estimates of projection methods for Navier–Stokes equations: first-order schemes, SIAM J. Numer. Anal., Volume 29 (1992), pp. 57-77

[7] J. Shen Remarks on the pressure error estimates for the projection methods, Numer. Math., Volume 67 (1994) no. 4, pp. 513-520

[8] R. Temam Behaviour at time t=0 of the solutions of semilinear evolution equations, J. Differential Equations, Volume 43 (1982) no. 1, pp. 73-92

  • F. Guillén-González; M.V. Redondo-Neble Convergence and error estimates of viscosity-splitting finite-element schemes for the primitive equations, Applied Numerical Mathematics, Volume 111 (2017), p. 219 | DOI:10.1016/j.apnum.2016.09.011
  • Xaverie L. Baxley-Hull U.S. Virgin Islands, Attorney-Client Privilege in the Americas (2017), p. 493 | DOI:10.1017/9781316759882.033
  • F. Guillén-González; M.V. Redondo-Neble Optimal first-order error estimates of a fully segregated scheme for the Navier–Stokes equations, Journal of Computational and Applied Mathematics, Volume 321 (2017), p. 348 | DOI:10.1016/j.cam.2017.02.025

Cité par 3 documents. Sources : Crossref

⁎ The first author has been partially supported by project BFM2003-06446-C02-01 and the second one by the research group FQM-315 of Junta de Andalucía.

Commentaires - Politique