In this paper, the nonconforming virtual element method is studied to solve a hemivariational inequality problem for the stationary Stokes equations with a nonlinear slip boundary condition. The nonconforming virtual elements enriched with polynomials on slip boundary are used to discretize the velocity, and discontinuous piecewise polynomials are used to approximate the pressure. The inf-sup condition is shown for the nonconforming virtual element method. An error estimate is derived under appropriate solution regularity assumptions, and the error bound is of optimal order when lowest-order virtual elements for the velocity and piecewise constants for the pressure are used. A numerical example is presented to illustrate the theoretically predicted convergence order.

本文研究了非协调虚拟元方法，以解决带有非线性滑动边界条件的平稳斯托克斯方程的半变分不等式问题。在滑移边界上用多项式丰富的不合格虚拟元素用于离散速度，不连续的分段多项式用于逼近压力。显示了非合格虚拟元素方法的inf-sup条件。在适当的求解规律性假设下得出误差估计，并且当使用速度的最低阶虚拟元素和压力的分段常数时，误差范围为最佳阶。给出了一个数值示例来说明理论上预测的收敛顺序。