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.