[Formulation mixte pour le problème de Stokes avec frottement de Tresca]
Dans cette note, nous proposons une formulation mixte à trois champs pour résoudre le problème de Stokes avec des conditions aux limites non-linéaires, du type Tresca. Deux multiplicateurs de Lagrange sont utilisés afin d'imposer et de régulariser la fonctionnelle énergie. Le problème résultant est approché à l'aide des éléments finis P1 bulle/P1-P1. Une estimation optimale est obtenue et un test numérique de validation est réalisé.
In this Note we propose and study a three field mixed formulation for solving the Stokes problem with Tresca-type nonlinear boundary conditions. Two Lagrange multipliers are used to enforce constraint and to regularize the energy functional. The resulting problem is discretized using P1 bubble/P1-P1 finite elements. Optimal error estimate is derived and a numerical validation test is achieved.
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@article{CRMATH_2010__348_19-20_1069_0,
author = {Ayadi, Mekki and Gdoura, Mohamed Khaled and Sassi, Taoufik},
title = {Mixed formulation for {Stokes} problem with {Tresca} friction},
journal = {Comptes Rendus. Math\'ematique},
pages = {1069--1072},
publisher = {Elsevier},
volume = {348},
number = {19-20},
year = {2010},
doi = {10.1016/j.crma.2010.10.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.10.001/}
}
TY - JOUR AU - Ayadi, Mekki AU - Gdoura, Mohamed Khaled AU - Sassi, Taoufik TI - Mixed formulation for Stokes problem with Tresca friction JO - Comptes Rendus. Mathématique PY - 2010 SP - 1069 EP - 1072 VL - 348 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.10.001/ DO - 10.1016/j.crma.2010.10.001 LA - en ID - CRMATH_2010__348_19-20_1069_0 ER -
%0 Journal Article %A Ayadi, Mekki %A Gdoura, Mohamed Khaled %A Sassi, Taoufik %T Mixed formulation for Stokes problem with Tresca friction %J Comptes Rendus. Mathématique %D 2010 %P 1069-1072 %V 348 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.10.001/ %R 10.1016/j.crma.2010.10.001 %G en %F CRMATH_2010__348_19-20_1069_0
Ayadi, Mekki; Gdoura, Mohamed Khaled; Sassi, Taoufik. Mixed formulation for Stokes problem with Tresca friction. Comptes Rendus. Mathématique, Tome 348 (2010) no. 19-20, pp. 1069-1072. doi : 10.1016/j.crma.2010.10.001. http://www.numdam.org/articles/10.1016/j.crma.2010.10.001/
[1] M. Ayadi, M.K. Gdoura, T. Sassi, Error estimates for Stokes problem with Tresca friction condition, Rapport de recherche, Lab. de Mathématiques Nicolas Oresme, 2010 – 4. 17 Mar 2010. | arXiv
[2] Mixed finite element approximation of 3D contact problem with given friction: Error analysis and numerical realization, M2AN, Volume 38 (2004) no. 3, pp. 563-578
[3] Wall slip of molten high density polyethylene. I. Sliding plate rheometer studies, J. Rheology, Volume 35 (1991) no. 4, pp. 497-523
[4] Calcul Scientifique avec Matlab, Ellipses, 2009
[5] Penalty finite element method for Stokes problem with nonlinear slip boundary conditions, J. Applied Mathematics and Computation, Volume 204 (2008), pp. 216-226
[6] Shear rheometry of fluids with a yield stress, J. Non-Newtonian Fluid Mech., Volume 23 (1987), pp. 91-106
[7] The effect of the slip boundary condition on the flow of fluids in a channel, Acta Mechanica, Volume 135 (1999), pp. 113-126
[8] Block copolymer extrusion distortions: Exit delayed transversal primary cracks and longitudinal secondary cracks: Extrudate splitting and continuous peeling, J. Non-Newtonian Fluid Mech., Volume 131 (2005), pp. 1-21
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