Djoko, J.K. (Jules Kamdem)Lubuma, Jean M.-S.Mbehou, M.2016-06-212016-12Djoko, J.K., Lubuma, J.M. & Mbehou, M. On the numerical solution of the stationary power-law Stokes equations : a penalty nite element approach. Journal of Scientific Computing (2016) 69: 1058-1082. doi:10.1007/s10915-016-0227-4.0885-7474 (print)1573-7691 (online)10.1007/s10915-016-0227-4http://hdl.handle.net/2263/53271In this work, we study the penalty finite element approximation of the stationary power law Stokes problem. We prove uniform convergence of the finite element solution with respect to the penalized parameter under classical assumptions on the weak solution. We formulate and analyze the convergence of a nonlinear saddle point problem by adopting a particular algorithm based on vanishing viscosity approach and long time behavior of an initial value problem. Finally, the predictions observed theoretically are validated by means of numerical experiments.en© Springer Science + Business Media New York 2016. The original publication is available at : http://link.springer.com/journal/10915.Power-law Stokes equationsPenalty finite element methodUniform convergenceAlgorithmInitial value problemInitial flowPostprint Article