The Superconvergence Phenomenon and Proof of the MAC Scheme for the Stokes Equations on Non-uniform Rectangular Meshes

An essential feature of the studied scheme is that the (discrete) kinetic energy remains controlled. We show the compactness of approximate sequences of solutions thanks to a

Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity.. Nonhomogeneous viscous incompressible fluids: existence

The obtained stability result provides a control of the pressure in L r (Ω), r < 2, from the discrete W −1,r norm of its gradient; besides the model problem detailed here, it may

This discretization enjoys the property that the integral over the computational domain Ω of the (discrete) dissipation term is equal to what is obtained when taking the inner

However, this is no longer true if a non uniform mesh is used, even in the conforming case; indeed, in this latter case, the Vorono¨ı cells V σ (k) are again rectangles, but they

In both cases (nonlinear centered and upstream weighting schemes), we prove the convergence of a penalized version of the scheme to a weak solution of the problem... As we noted in

Adapting at the discrete level the arguments of the recent theory of compressible Navier-Stokes equations [17, 6, 20], we prove the existence of a solution to the discrete

Abstract We propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier-