Stable finite-element calculation of incompressible flows using the rotation form of convection

Conforming finite-element approximations are considered for the incompressible Navier-Stokes equations with nonlinear terms written in the convection or rotation forms. Implicit time integration results in nice stability properties of auxiliary problems which can be solved by efficient numerical algorithms. The original nonlinear system admits relatively simple stabilization strategies. The paper presents in a unified form the convergence analysis, including the design of stabilization parameters, for linearized equations in both convection and rotation forms. Moreover, it is shown that a Galerkin discretization of the pressure-regularized Oseen problem with skew-symmetric terms in rotation form possesses better stability properties and, being much easier to solve, can be used as a predictor in implicit calculations.