Optimal first-order error estimates of a fully segregated scheme for the Navier–Stokes equations

Abstract

A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier–Stokes equations in three-dimensional domains. This scheme is based on an incremental pressure projection method and decouples each component of the velocity and the pressure, solving in each time step, a linear convection–diffusion problem for each component of the velocity and a Poisson–Neumann problem for the pressure.Using an inf–sup stable and continuous finite-elements approach of order O(h) in space, unconditional optimal error estimates of order O(k+h) are deduced for velocity and pressure (without imposing constraints on the mesh size h and the time step k).Finally, some numerical results are performed to validate the theoretical analysis, and also to compare the studied scheme with other current first-order segregated schemes.