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

This paper is a presentation of a mixed spectral element method, based on s taggered grids strategy, used for the discretization of second-order ellipt ic problems set under hybrid dual formulation. A numerical analysis is perf ormed proving the expected optimality and some numerical tests are describe d to confirm the predicted convergence rates. The second part deals with a high-order time splitting/spectral scheme for the simulation of unsteady in compressible Navier-Stokes flows. We show how to use such a server as a fil tering tool to obtain divergence free discrete velocity. Some computational examples are reported which quantify the improvements, induced by such a B iter, we have observed: a strengthening of the stability and of the accurac y (C) 1998 Elsevier Science S.A. All rights reserved.