CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM
                  UNIVERSITY OF COLORADO AT DENVER


TITLE:   Employing ``bubbles'' in the FEM approximation of 
         convection-diffusion problems

SPEAKER: Alessandro Russo
         Istituto di Analisi Numerica del CNR
         Pavia, Italy

DATE:    Wednesday, September 21, 1994

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    2:30 pm (Refreshments served at 2:15 pm)

ABSTRACT: We consider in this talk the finite element approximation of
convection-diffusion problems. As it is well known, when convection dominates 
over diffusion the classical finite element methods don't work: the 
centered-type discretization of the convective term generates spurious 
oscillations that can pollute the whole numerical solution.
This difficulty has been overcome by the so-called Streamline-Upwind
Petrov/Galerkin method (SUPG), which introduces artificial
diffusion in the transport direction without upsetting consistency.
Recently a close relationship between SUPG and the so-called
``virtual bubble method'' has been discovered.
We will describe the ``upwind'' bubbles, which reproduce the right 
coefficients for SUPG, and we will discuss the role played by the 
bubbles in the theory of a posteriori error indicators.