Abstract
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.
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