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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 and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane

Antonio Greco, Giuseppe Viglialoro (2023)

Applications of Mathematics

This paper deals with a mixed boundary-value problem of Ventcel type in two variables. The peculiarity of the Ventcel problem lies in the fact that one of the boundary conditions involves second order differentiation along the boundary. Under suitable assumptions on the data, we first give the definition of a weak solution, and then we prove that the problem is uniquely solvable. We also consider a particular case arising in real-world applications and discuss the resulting model.

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