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

Serge Nicaise ^{This paper is concerned with the mixed formulation of the Navier–Stokesequations with mixed boundary conditions in 2D polygonal domainsand its numerical approximation. We first describe the regularityof any solution. The problem is then approximated by a mixedfinite-element method where the strain tensor and the antisymmetricgradient tensor, quantities of practical importance, are introducedas new unknowns. An existence result for the finite-elementsolution and convergence results are proved near a nonsingularsolution. Quasi-optimal error estimates are finally presented.}