Error estimates for Stokes problem with Tresca friction conditions
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 5, p. 1413-1429

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.

DOI : https://doi.org/10.1051/m2an/2014001
Classification:  45N30,  76D07,  35J87,  35M87
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {48},
number = {5},
year = {2014},
pages = {1413-1429},
doi = {10.1051/m2an/2014001},
mrnumber = {3264359},
language = {en},
url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 5, pp. 1413-1429. doi : 10.1051/m2an/2014001. http://www.numdam.org/item/M2AN_2014__48_5_1413_0/

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