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.

翻译：本文针对具有摩擦型非线性滑移边界条件的Stokes流动问题，提出了一种稳定化有限元格式。该边界条件通过引入额外的拉格朗日乘子进行施加，所提出的稳定化格式同时实现了对压力场和拉格朗日乘子的联合稳定化处理。我们建立了稳定性分析和先验误差估计，并通过数值收敛性研究验证了理论分析结果。