Djoko, J.K. (Jules Kamdem)Koko, Jonas2016-05-112016-06Djoko, J & Koko, J 2016, 'Numerical methods for the Stokes and Navier-Stokes equations driven by threshold slip boundary conditions', Computer Methods in Applied Mechanics and Engineering, vol. 305, pp. 936-958.0045-7825 (print)1879-2138 (online)10.1016/j.cma.2016.03.026http://hdl.handle.net/2263/52589In this article, we discuss the numerical solution of the Stokes and Navier-Stokes equations completed by nonlinear slip boundary condi- tions of friction type in two and three dimensions. To solve the Stokes system, we rst reduce the related variational inequality into a saddle point-point problem for a well chosen augmented Lagrangian. To solve this saddle point problem we suggest an alternating direction method of multiplier together with nite element approximations. The solution of the Navier Stokes system combines nite element approximations, time discretization by operator splitting and augmented Lagrangian method. Numerical experiment results for two and three dimensional ow con rm the interest of these approaches.en© 2016 Elsevier B.V. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, vol. 305, pp. 936-958, 2016. doi : 10.1016/j.cma.2016.03.026.Nonlinear slip boundary conditionStokes equationsNavier Stokes equationsVariational inequalityAugmented LagrangianAlternating direction method of multipliersMarchuk-Yanenko's scheme3d-simulationsPostprint Article