An L2‐stable approximation of the Navier–Stokes convection operator for low‐order non‐conforming finite elements

Abstract

Abstract We develop in this paper a discretization for the convection term in variable density unstationary Navier–Stokes equations, which applies to low‐order non‐conforming finite element approximations (the so‐called Crouzeix–Raviart or Rannacher–Turek elements). This discretization is built by a finite volume technique based on a dual mesh. It is shown to enjoy an L 2 stability property, which may be seen as a discrete counterpart of the kinetic energy conservation identity. In addition, numerical experiments confirm the robustness and the accuracy of this approximation; in particular, in L 2 norm, second‐order space convergence for the velocity and first‐order space convergence for the pressure are observed. Copyright © 2010 John Wiley & Sons, Ltd.