This paper on "Stable and Robust Basis Functions for the Solution of the Navier-Stokes Equations Using the Generalized FEM" was presented at the NAFEMS World Congress on Effective Engineering Analysis - 25-28 April 1999, Newport, Rhode Island, USA.

Abstract

The Generalized Finite Element Method (GFEM) is used to solve the incompressible Navier-Stokes equations with mixed, augmented Lagrangian, and penalty formulations; convergence analysis, stability estimates, and implementation details are presented. It is shown that the GFEM is well suited to incorporate particular solutions of the governing equations as basis functions, such as locally divergence free polynomial basis. This technique is also well suited to resolve localized flow patterns through the use of polynomial enrichments, and delivers optimal order of accuracy in accordance with the order of the basis functions.
Analytical studies and numerical experiments demonstrate that the method is robust and capable of delivering high rates of convergence.