An L2-stable approximation of the Navier-Stokes convection operator for low-order non-conforming finite elements
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 (C) 2010 John Wiley & Sons, Ltd.
stability kinetic energy theorem rannacher-turek finite element crouzeix-raviart finite element low mach number flows incompressible flows