Stabilised finite element method for Stokes problem with nonlinear slip condition

2023/08/29 by Tom Gustafsson, Gustafsson, Tom, Juha Videman +1
Computer Science · Engineering · Mathematics · #65N12 #65N30 #76M10 #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2308.15182

openalex publication_date 2023/08/29 · openalex created_date 2023/08/31 · openalex updated_date 2026/07/28

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.

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