A difference-scheme with error $O(\tau^2+|h|^2)$ for a Navier–Stokes system

A system of quasilinear equations of parabolic type which approximates a nonstationary Navier–Stokes problem is considered in this article. Triple layered implicit difference schemes with a linear operator on the upper layer are constructed for this system. Rapidly converging iterative methods can be applied to find a solution on the upper layer. It is proved that the proposed scheme has error $O(\tau^2+|h|^2)$.