A stabilized finite element method for generalized stationary incompressible flows

✍ Scribed by Ramon

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 979 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(00)00260-7

✦ Synopsis

In this paper, we describe a ®nite element formulation for the numerical solution of the stationary incompressible Navier±Stokes equations including Coriolis forces and the permeability of the medium. The stabilized method is based on the algebraic version of the sub-grid scale approach. We ®rst describe this technique for general systems of convection±diusion±reaction equations and then we apply it to the linearized ¯ow equations. The important point is the design of the matrix of stabilization parameters that the method has. This design is based on the identi®cation of the stability problems of the Galerkin method and a scaling of variables argument to determine which coecients must be included in the stabilization matrix. This, together with the convergence analysis of the linearized problem, leads to a simple expression for the stabilization parameters in the general situation considered in the paper. The numerical analysis of the linearized problem also shows that the method has optimal convergence properties.