A Posteriori Error Estimator for Mixed Approximation of the Navier-Stokes Equations with the Boundary Condition

In this paper, we introduce the Navier-Stokes equations with a new boundary condition. In this context, we show the existence and uniqueness of the solution of the weak formulation associated with the proposed problem. To solve this latter, we use the discretization by mixed finite element method. In addition, two types of a posteriori error indicator are introduced and are shown to give global error estimates that are equivalent to the true error. In order to evaluate the performance of the method, the numerical results are compared with some previously published works and with others coming from commercial code like ADINA system. Keywords—Navier-Stokes Equations; c b a C , , boundary condition; Mixed Finite element method; Residual Error Estimator;