Analysis of estimators for Stokes problem using a mixed approximation

In this work, we introduce the steady Stokes equations with a new boundary condition, generalizes Dirichlet and Neumann conditions. Then derive an adequate variational formulation of equations. It includes algorithms for discretization by mixed finite element methods. We use block diagonal preconditioners problem. obtain faster convergence when applying preconditioned MINRES method. Two types posteriori error indicator are introduced shown to give global estimates that equivalent true error. order evaluate performance method, numerical results compared some previously published works or others coming from commercial code like Adina system.