A generalization of Uzawa's algorithm for the solution of the Navier‐Stokes equations

Abstract Usawa's algorithm provides an efficient method for solving the divergence‐free Stokes problem. On the other hand, the Newton–Raphson scheme is very popular for the solution of the nonlinear Navier–Stokes equations. We propose here a new method that combines these two algorithms and converges to a divergence‐free solution of the nonlinear Navier–Stokes equations.