UNIVERSITY OF COLORADO AT DENVER
PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver
TIME: NOON (Refreshments served at 11:45 am)
DATE: November 29, 1999
TITLE: Approximating the incompressible Navier Stokes equations using a two level finite element method BY Ali Ihsan NESLITURK Department of Mathematics, University of Colorado at Denver ABSTRACT: We consider the Galerkin finite element method for the incompressible Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble (RFB) functions. We show that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrangular elements. To find the bubble part of the solution, a two-level finite element method (TLFEM) is described and its application to the Navier-Stokes equation is displayed. Numerical solutions employing the TLFEM are presented for three benchmark problems. We compare the numerical solutions using the TLFEM with the numerical solutions using a stabilized method.