Workshop Numerical Analysis for Singularly Perturbed Problems
(dedicated to the 60th birthday of Martin Stynes)

Workshop Singularly Perturbed Problems

Talks & Slides

Convergence results in balanced norms for singularly perturbed problems

Sebastian Franz (Institut für Numerik, TU-Dresden)

We consider singularly perturbed problems of reaction-diffusion and convection-diffusion type, specifically with parabolic boundary layers for the latter. In these cases good convergence results for bilinear elements on layer adapted meshes are known in the natural energy norm. Nevertheless, this norm is known to be too weak to recognise all boundary layers of our problems.
We present robust convergence results obtained in stronger norms—so called balanced norms—that overcome this drawback. Hereby the weight of the H1-seminorm component is properly adjusted, s.t. all boundary layers contribute to the balanced norm.

Last change: 21 November 2011