Convergence rate estimates for a projection-difference scheme as applied to the nonstationary stokes equation in cylindrical coordinates

An implicit projection-difference scheme is constructed for the nonstationary Stokes equation in cylindrical coordinates. No axial symmetry is assumed. Under minimal assumptions about the initial data, convergence rate estimates are obtained that are uniform in the inner radius of the domain of order $(\tau^{1/2}+h)^\alpha$, $\alpha=1$, $2$. The results remain valid for domains with no hole and in the case of Cartesian coordinates.