We discuss how slip conditions for the Stokes equation can be handled using Nitsche method, for a stabilized finite element discretization. Emphasis is made on the interplay between stabilization and Nitsche terms. Well-posedness of the discrete problem and optimal convergence rates, in natural norm for the velocity and the pressure, are established, and illustrated with various numerical experiments. The proposed method fits naturally in the context of a finite element implementation while being accurate, and allows an increased flexibility in the choice of the finite element pairs.

翻译：本文探讨如何采用Nitsche方法处理Stokes方程的滑移条件，针对稳定化有限元离散格式。重点分析稳定化项与Nitsche项之间的相互作用。我们建立了离散问题的适定性，并在速度和压力的自然范数下证明了最优收敛速率，同时通过多种数值实验加以验证。所提出的方法在保持精度的同时，自然适配有限元实现框架，并提高了有限元对选择时的灵活性。