Summary: We consider two-dimensional time-dependent Navier-Stokes equations in a rectangular domain and study the method of full splitting [see, e.g., A. J. Chorin, Math. Comput. 23, 341–353 (1969; Zbl 0184.20103)]. On the physical level, this problem is splitted into two processes: convection-diffusion and action of pressure. The convection-diffusion step is further splitted in two geometric directions. To implement the finite element method, we use the approach with uniform square grids which are staggered relative to one another. This allows the Ladyzhenskaya-Babuska-Brezzi condition for stability of pressure to be fulfilled without usual diminishing the number of degrees of freedom for pressure relative to that for velocities. For pressure, we take piecewise constant finite elements. As for velocities, we use piecewise bilinear elements.
For the entire collection see [Zbl 1059.76002].