Stabilized Finite Element Schemes for Incompressible Flow Using Velocity/Pressure Spaces Satisfying the LBB-Condition

摘要

We discuss a stabilized finite element method for the computation of incompressible flow using velocity/pressure spaces that satisfy the inf-sup condition. The idea is to obtain stability by adding a least squares term penalizing the jump in the gradient or the streamline derivative over element boundaries to the standard Galerkin formulation. The key feature of this method is that, unlike the SUPG method, no artificial velocity-pressure couplings are introduced. We show that in order to obtain optimal order a priori error estimates independent of the Reynolds number we must add a least squares term giving additional control of the incompressibility condition. Assuming that the velocity/pressure spaces satisfies the inf-sup condition we then prove optimal order a priori error estimates in an H(div) dominated triple norm using the Fortin criterion. We illustrate the theory with a numerical example.