Explicit solution of the incompressible Navier–Stokes equations with linear finite elements

A three-field finite element scheme for the explicit iterative solution of the stationary incompressible Navier–Stokes equations is studied. In linearized form the scheme is associated with a generalized time-dependent Stokes system discretized in time. The resulting system of equations allows for a stable approximation of velocity, pressure and stress deviator tensor, by means of continuous piecewise linear finite elements, in both two- and three-dimensional space. Convergence in an appropriate sense applying to this finite element discretization is demonstrated, for the stationary Stokes system.