[Un schéma volumes finis centrés par mailles pour la résolution des équations de Stokes sur des maillages 2D généraux]
On présente ici une nouvelle méthode de volumes finis pour la discrétisation des équations de Stokes sur un maillage 2D non structuré. On présente un résultat de convergence, ainsi qu'une estimation d'erreur dans le cas où la solution est suffisamment régulière.
This Note presents a new finite volume scheme for the Stokes equations on general non-structured meshes. A convergence result is presented, and an error estimate is given when the solution is regular enough.
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@article{CRMATH_2003__337_2_125_0,
author = {Eymard, Robert and Herbin, Rapha\`ele},
title = {A cell-centered finite volume scheme on general meshes for the {Stokes} equations in two space dimensions},
journal = {Comptes Rendus. Math\'ematique},
pages = {125--128},
publisher = {Elsevier},
volume = {337},
number = {2},
year = {2003},
doi = {10.1016/S1631-073X(03)00266-8},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00266-8/}
}
TY - JOUR AU - Eymard, Robert AU - Herbin, Raphaèle TI - A cell-centered finite volume scheme on general meshes for the Stokes equations in two space dimensions JO - Comptes Rendus. Mathématique PY - 2003 SP - 125 EP - 128 VL - 337 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00266-8/ DO - 10.1016/S1631-073X(03)00266-8 LA - en ID - CRMATH_2003__337_2_125_0 ER -
%0 Journal Article %A Eymard, Robert %A Herbin, Raphaèle %T A cell-centered finite volume scheme on general meshes for the Stokes equations in two space dimensions %J Comptes Rendus. Mathématique %D 2003 %P 125-128 %V 337 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00266-8/ %R 10.1016/S1631-073X(03)00266-8 %G en %F CRMATH_2003__337_2_125_0
Eymard, Robert; Herbin, Raphaèle. A cell-centered finite volume scheme on general meshes for the Stokes equations in two space dimensions. Comptes Rendus. Mathématique, Tome 337 (2003) no. 2, pp. 125-128. doi : 10.1016/S1631-073X(03)00266-8. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00266-8/
[1] Ph. Blanc, R. Eymard, R. Herbin, An error estimate for finite volume methods for the Stokes equations, LATP preprint, 2002, Université Aix-Marseille 1
[2] R. Eymard, T. Gallouët, R. Herbin, Finite volume methods, in: P.G. Ciarlet, J.-L. Lions (Eds.), Handbook of Numerical Analysis, Vol. VII, North-Holland, pp. 713–1020
[3] R. Eymard, R. Herbin, A finite volume scheme on general meshes for the Stokes equations in two-space dimensions, LATP preprint, 2003, Université Aix-Marseille 1
[4] Finite Element Methods for the Navier–Stokes Equations: Theory and Algorithms, Springer, Berlin, 1986
[5] Analysis and convergence of the MAC scheme II, Navier–Stokes equations, Math. Comp., Volume 65 (1996), pp. 29-44
[6] Numerical heat transfer and fluid flow (Minkowycz; Sparrow, eds.), Series in Computational Methods in Mechanics and Thermal Sciences, McGraw-Hill, 1980
[7] Navier–Stokes Equations (Lions, J.-L.; Papanicolaou, G.; Rockafellar, R.T., eds.), Stud. Math. Appl., North-Holland, 1977
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