Djoko, J.K. (Jules Kamdem)2017-05-102017-04J. K. Djoko (2017) Convergence Analysis of the Nonconforming Finite Element Discretization of Stokes and Navier –Stokes Equations with Nonlinear Slip Boundary Conditions, Numerical Functional Analysis and Optimization, 38:8, 951-987, DOI: 10.1080/01630563.2017.1316992.0163-0563 (print)1532-2467 (online)10.1080/01630563.2017.1316992http://hdl.handle.net/2263/60307This work is concerned with the nonconforming finite approximations for the Stokes and Navier-Stokes equations driven by slip boundary condition of “friction” type. It is well documented that if the velocity is approximated by the Crouzeix-Raviart element of order one, while the discrete pressure is constant element wise the inequality of Korn doe not hold. Hence we propose a new formulation taking into account the curvature and the contribution of tangential velocity at the boundary. Using the maximal regularity of the weak solution, we derive a priori error estimates for the velocity and pressure by taking advantage of the enrichment mapping and the application of Babuska-Brezzi’s theory for mixed problems.en© Taylor and Francis Group, LLC. This is an electronic version of an article published in Numerical Functional Analysis and Optimization, 38:8, 951-987, 2017. DOI: 10.1080/01630563.2017.1316992. Numerical Functional Analysis and Optimization is available online at : http://www.tandfonline.comloi/lnfa20.Stokes equationsNavier-Stokes equationsNonlinear slip boundary conditionsVariational inequalityCrouzeix-Raviart elementA priori error estimatePostprint Article