On some finite-difference approximations of Stokes problem

Several finite-difference schemes for the Stokes problem satisfying the Ladyzhenskaya–Babuska–Brezzi condition are considered. These schemes use staggered meshes (MAC–schemes) in rectangular domains. The aim of investigations is to obtain a dependence of a constant in the LBB–condition on geometric and grid parameters for a scheme and a comparative analysis of schemes with respect to the data obtained. Discrete eigenvalue problems were solved with high precision. Results of some three-dimensional calculations are presented.