Stabilised finite element method for Stokes problem with nonlinear slip condition

TL;DR

This paper presents a stabilised finite element method for solving Stokes flow problems with nonlinear slip boundary conditions, incorporating a Lagrange multiplier and providing stability, error analysis, and numerical verification.

Contribution

It introduces a novel stabilised finite element formulation for Stokes problems with nonlinear slip conditions, including stability analysis and convergence verification.

Findings

The method is stable and convergent.

Numerical results verify theoretical error estimates.

Effective enforcement of nonlinear slip boundary conditions.

Abstract

This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier and the stabilised formulation is based on simultaneously stabilising both the pressure and the Lagrange multiplier. We establish the stability and the a priori error analyses, and perform a numerical convergence study in order to verify the theory.