Portland State University
Fariborz Maseeh Department of Mathematics & Statistics
The Maseeh Mathematics and Statistics Colloquium Series*
Douglas N. Arnold
~School of Mathematics,
University of Minnesota ~
Stability, Consistency, and Convergence: Modern Variations on a Classical Theme
Consistency and stability of numerical discretizations are the basic leitmotifs of numerical analysis, and the idea that consistency and stability imply convergence is a principle theme, particularly in the numerical solution of partial differential equations. But both consistency and stability can, in some situations, be more subtle and elusive than they might appear. Even seemingly simple examples of numerical discretizations can yield unexpected--and even, in real life applications, tragic--results. The development of consistent, stable numerical methods remains elusive for important classes of problems. We will survey these ideas from their origins in the precomputer era to the present day, via a variety of examples. We finish by describing a new approach, the finite element exterior calculus, which borrows tools from geometry and topology to design and elucidate stable finite element methods.
Monday, May 10th, 2010, 3:00pm
Smith Memorial Student Union Room 228
(Refreshments served at 3:00 in hallway)
* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU. This event is free and open to the public.