Error estimates for Stokes problem with Tresca friction condition

TL;DR

This paper introduces a new mixed finite element formulation for the Stokes problem with Tresca friction, providing error estimates and numerical validation for the approach.

Contribution

It proposes a novel three-field mixed formulation with specific finite elements for the Stokes problem under Tresca boundary conditions, including error analysis.

Findings

Error estimates for the proposed formulation are derived.

Numerical studies confirm the theoretical error bounds.

The method effectively handles non-linear Tresca boundary conditions.

Abstract

In this work we propose and study a three field mixed formulation for solving the Stokes problem with Tresca-type non-linear boundary conditions. Two Lagrange multipliers are used to enforce div(u)=0 constraint and to regularize the energy functional. The resulting problem is discretised using "P1 bubble/P1-P1" finite elements. Error estimates are derived and several numerical studies are achieved.