On a Galerkin--Lagrange Multiplier Method for the Stationary Navier--Stokes Equations

A Galerkin–Lagrange multiplier formulation is used for the numerical solution of the stationary Navier–Stokes equations, in order to avoid the construction of zero-divergence elements. The formulation is based on different approximating spaces for the velocity field and the pressure. Optimal rate of convergence estimates are derived. Moreover, a Galerkin–Newton scheme for the solution of the nonlinear equations is shown to be quadratically locally convergent. Another scheme is shown to be linearly globally convergent.