# Error estimates for Stokes problem with Tresca friction conditions

Mekki Ayadi; Leonardo Baffico; Mohamed Khaled Gdoura; Taoufik Sassi

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

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topAyadi, 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>.

@article{Ayadi2014,

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 - 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 - 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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