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In this article, a blood flow model of arteriosclerosis, which is governed by the incompressible Navier–Stokes equations with nonlinear slip boundary conditions, is constructed and analyzed. By means of suitable numerical integration approximation for the nonlinear boundary term in this model, a discrete variational inequality for the model based on math formula stabilized finite elements is proposed. Optimal order error estimates are obtained. Finally, numerical examples are shown todoi:10.11575/prism/35035 fatcat:uisd4pxxkrcaljdwglhwtleeq4