Optimal first-order error estimates of a fully segregation scheme for the Navier-Stokes equations
Provides rigorous error analysis for a practical segregated scheme for incompressible Navier-Stokes equations, but the method and results are incremental extensions of existing projection methods.
The paper proves optimal first-order error estimates of order O(k+h) for a fully segregated scheme for the Navier-Stokes equations, using an incremental pressure projection method with inf-sup stable finite elements, without constraints on mesh size and time step.
A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, 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 first-order \emph{inf-sup} stable $C^0$-finite elements, optimal error estimates of order $O(k+h)$ are deduced without imposing constraints on $h$ and $k$, the mesh size and the time step, respectively. Finally, some numerical results are presented according the theoretical analysis, and also comparing to other current first-order segregated schemes.