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.