Brigitte Métivet

A high‐order characteristics/finite element method for the incompressible Navier‐Stokes equations

In this paper we consider a discretization of the incompressible Navier-Stokes equations involving a second-order time scheme based on the characteristics method and a spatial discretization of finite element type. Theoretical and numerical analyses are detailed and we obtain stability results abnd optimal eror estimates on the velocity and pressure under a time step restriction less stringent than the standard Courant-Freidrichs-Levy condition. Finally, some numerical results obtained wiht the code N3S are shown which justify the interest of this scheme and its advantages with respect to an analogous first-order time scheme.

A high order characteristics method for the incompressible Navier-Stokes equations

We analyze a high order characteristics method for the Navier—Stokes equations. We focus on the cases of the first, second and third order in time schemes with finite element spatial discretization. A numerical comparison between the first and second order schemes is done for steady or transient states flows.

Spectral approximation of the periodic-nonperiodic Navier-Stokes equations

SummaryIn order to approximate the Navier-Stokes equations with periodic boundary conditions in two directions and a no-slip boundary condition in the third direction by spectral methods, we justify by theoretical arguments an appropriate choice of discrete spaces for the velocity and the pressure. The compatibility between these two spaces is checked via an infsup condition. We analyze a spectral and a collocation pseudo-spectral method for the Stokes problem and a collocation pseudo-spectral method for the Navier-Stokes equations. We derive error bounds of spectral type, i.e. which behave likeM−σ whereM depends on the number of degrees of freedom of the method and σ represents the regularity of the data.

Explicit error bounds for a nonconforming finite element method

Let u be the solution of the following model:

Finite element approximations of viscous flows with varying density

\left\{\begin{array}{l} \mbox{find

Couplage des équations de Navier-Stokes et de la chaleur : le modèle et son approximation par éléments finis

u \in H^1_0(\Omega)

Single-grid spectral collocation for the Navier-Stokes equations

such that} \\ [3pt] -\Delta u = f\quad\mbox{in } \Omega, \end{array}\right.

Error estimates for spectral approximation of Stokes equations

where f is a given function in L2(\Omega)