UNIVERSITY OF COLORADO AT DENVER

PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver

TIME: 2 pm (Refreshments served at 1:45 pm)

DATE: August 10 1999

The Streamline-Diffusion Finite Element Method on an a-priori
       adapted Mesh for a Convection-Diffusion Problem
                   with Exponential Layers


                         Lutz Tobiska
            
           Otto-von-Guericke Universitaet Magdeburg
               Institut fuer Analysis und Numerik 
          Postfach 4120 , Magdeburg, D-39016, Germany 


On the unit square, we consider a singularly perturbed
convection-diffusion boundary value problem whose solution has two
exponential boundary layers. We apply the streamline-diffusion finite 
element method with piecewise bilinear trial functions on an a-priori 
adapted piecewise uniform mesh and show that it is convergent, 
uniformly in the diffusion parameter in the usual streamline-diffusion
norm. As a corollary we get convergence uniformly in the diffusion
parameter in the local maximum norm on the fine part of the mesh (i.e.,
inside the boundary layers). This shows that the streamline-diffusion
finite element method combines good stability properties with high
accuracy on layer adapted grids also inside the layers.


=================================================================
Prof. Dr. Lutz Tobiska                   | 
Otto-von-Guericke Universitaet Magdeburg | Tel: +49-391-67 18650
Institut fuer Analysis und Numerik       |
Postfach 4120 , Magdeburg, D-39016       | Fax: +49-391-67 18073 

email: tobiska@mathematik.uni-magdeburg.de
www: http://david.math.uni-magdeburg.de/home/tobiska/