Error estimates for Stokes problem with Tresca friction conditions
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 48 (2014) no. 5, pp. 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
Mots clés : Stokes problem, Tresca friction, variational inequality, mixed finite element, error estimates
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author = {Ayadi, Mekki and Baffico, Leonardo and Gdoura, Mohamed Khaled and Sassi, Taoufik},
title = {Error estimates for {Stokes} problem with {Tresca} friction conditions},
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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, Tome 48 (2014) no. 5, pp. 1413-1429. doi : 10.1051/m2an/2014001. http://archive.numdam.org/articles/10.1051/m2an/2014001/

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