Staggered grids hybrid-dual spectral element method for second-order elliptic problems application to high-order time splitting methods for Navier-Stokes equations Original Research Article

This paper is a presentation of a mixed spectral element method, based on staggered grids strategy, used for the discretization of second-order elliptic problems set under hybrid dual formulation. A numerical analysis is performed proving the expected optimality and some numerical tests are described to confirm the predicted convergence rates. The second part deals with a high-order time splitting/spectral scheme for the simulation of unsteady incompressible Navier-Stokes flows. We show how to use such a solver as a filtering tool to obtain divergence free discrete velocity. Some computational examples are reported which quantify the improvements, induced by such a filter, we have observed: a strengthening of the stability and of the accuracy.