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.
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.
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Francisco Guillén-González 1; María Victoria Redondo-Neble 2
@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/
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Cited by 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.
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