In this paper, we present and study a mixed variational method in order to approximate, with the finite element method, a Stokes problem with Tresca friction boundary conditions. These non-linear boundary conditions arise in the modeling of mold filling process by polymer melt, which can slip on a solid wall. The mixed formulation is based on a dualization of the non-differentiable term which define the slip conditions. Existence and uniqueness of both continuous and discrete solutions of these problems is guaranteed by means of continuous and discrete inf-sup conditions that are proved. Velocity and pressure are approximated by P1 bubble-P1 finite element and piecewise linear elements are used to discretize the Lagrange multiplier associated to the shear stress on the friction boundary. Optimal a priori error estimates are derived using classical tools of finite element analysis and two uncoupled discrete inf-sup conditions for the pressure and the Lagrange multiplier associated to the fluid shear stress.
Mots clés : Stokes problem, Tresca friction, variational inequality, mixed finite element, error estimates
@article{M2AN_2014__48_5_1413_0,
author = {Ayadi, Mekki and Baffico, Leonardo and Gdoura, Mohamed Khaled and Sassi, Taoufik},
title = {Error estimates for {Stokes} problem with {Tresca} friction conditions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1413--1429},
publisher = {EDP-Sciences},
volume = {48},
number = {5},
year = {2014},
doi = {10.1051/m2an/2014001},
mrnumber = {3264359},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014001/}
}
TY - JOUR AU - Ayadi, Mekki AU - Baffico, Leonardo AU - Gdoura, Mohamed Khaled AU - Sassi, Taoufik TI - Error estimates for Stokes problem with Tresca friction conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1413 EP - 1429 VL - 48 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014001/ DO - 10.1051/m2an/2014001 LA - en ID - M2AN_2014__48_5_1413_0 ER -
%0 Journal Article %A Ayadi, Mekki %A Baffico, Leonardo %A Gdoura, Mohamed Khaled %A Sassi, Taoufik %T Error estimates for Stokes problem with Tresca friction conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1413-1429 %V 48 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014001/ %R 10.1051/m2an/2014001 %G en %F M2AN_2014__48_5_1413_0
Ayadi, Mekki; Baffico, Leonardo; Gdoura, Mohamed Khaled; Sassi, Taoufik. Error estimates for Stokes problem with Tresca friction conditions. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 5, pp. 1413-1429. doi : 10.1051/m2an/2014001. http://www.numdam.org/articles/10.1051/m2an/2014001/
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