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tresca friction

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Error estimates for Stokes problem with Tresca frictionconditions
Mekki Ayadi, Leonardo Baffico, Mohamed Khaled Gdoura, Taoufik Sassi
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 48 / Issue 5 / September 2014

Published online by Cambridge University Press:

13 August 2014, pp. 1413-1429

Print publication:

September 2014
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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 bypolymer melt, which can slip on a solid wall. The mixed formulation is based on adualization of the non-differentiable term which define the slip conditions. Existence anduniqueness of both continuous and discrete solutions of these problems is guaranteed bymeans of continuous and discrete inf-sup conditions that are proved. Velocity and pressureare approximated by P1 bubble-P1 finite element and piecewise linearelements are used to discretize the Lagrange multiplier associated to the shear stress onthe friction boundary. Optimal a priori error estimates are derived usingclassical tools of finite element analysis and two uncoupled discrete inf-sup conditionsfor the pressure and the Lagrange multiplier associated to the fluid shear stress.