# Error estimates for Stokes problem with Tresca friction conditions

• Volume: 48, Issue: 5, page 1413-1429
• ISSN: 0764-583X

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## Abstract

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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.

## How to cite

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Ayadi, Mekki, et al. "Error estimates for Stokes problem with Tresca friction conditions." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.5 (2014): 1413-1429. <http://eudml.org/doc/273283>.

abstract = {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.},
author = {Ayadi, Mekki, Baffico, Leonardo, Gdoura, Mohamed Khaled, Sassi, Taoufik},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Stokes problem; Tresca friction; variational inequality; mixed finite element; error estimates},
language = {eng},
number = {5},
pages = {1413-1429},
publisher = {EDP-Sciences},
title = {Error estimates for Stokes problem with Tresca friction conditions},
url = {http://eudml.org/doc/273283},
volume = {48},
year = {2014},
}

TY - JOUR
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 - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 5
SP - 1413
EP - 1429
AB - 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.
LA - eng
KW - Stokes problem; Tresca friction; variational inequality; mixed finite element; error estimates
UR - http://eudml.org/doc/273283
ER -

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