A refined mixed finite-element method for the stationary Navier-Stokes equations with mixed boundary conditions

This paper is concerned with the mixed formulation of the Navier-Stokes equations with mixed boundary conditions in 2D polygonal domains and its numerical approximation. We first describe the regularity of any solution. The problem is then approximated by a mixed finite-element method where the strain tensor and the antisymmetric gradient tensor, quantities of practical importance, are introduced as new unknowns. An existence result for the finite-element solution and convergence results are proved near a nonsingular solution. Quasi-optimal error estimates are finally presented.