[Estimations optimales d'erreur d'une méthode de pas fractionnaire appliqué à des équations de Navier–Stokes 3D]
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.
Accepté le :
Publié le :
@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] 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] 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] On error estimates of projection methods for Navier–Stokes equations: first-order schemes, SIAM J. Numer. Anal., Volume 29 (1992), pp. 57-77
[7] Remarks on the pressure error estimates for the projection methods, Numer. Math., Volume 67 (1994) no. 4, pp. 513-520
[8] Behaviour at time of the solutions of semilinear evolution equations, J. Differential Equations, Volume 43 (1982) no. 1, pp. 73-92
Cité par Sources :
⁎ 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