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Error estimates for Stokes problem with Tresca friction conditions

Mekki Ayadi, Leonardo Baffico, Mohamed Khaled Gdoura, Taoufik Sassi (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Existence of a renormalized solution of nonlinear degenerate elliptic problems

Youssef Akdim, Chakir Allalou (2014)

Applicationes Mathematicae

We study a general class of nonlinear elliptic problems associated with the differential inclusion β ( u ) - d i v ( a ( x , D u ) + F ( u ) ) f in Ω where f L ( Ω ) . The vector field a(·,·) is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in function spaces we prove existence of renormalized solutions for general L -data.

Existence of solutions of degenerated unilateral problems with L 1 data

Lahsen Aharouch, Youssef Akdim (2004)

Annales mathématiques Blaise Pascal

In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type A u + g ( x , u , u ) = f - div F , where A is a Leray-Lions operator and g is a Carathéodory function having natural growth with respect to | u | and satisfying the sign condition. The second term is such that, f L 1 ( Ω ) and F Π i = 1 N L p ( Ω , w i 1 - p ) .

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