Thursday, February 9, 9:30 am in room MTH 3206, University of Maryland,
College Park
Some New Results in Numerical Analysis of Conservation Laws
Dr. Pierre Gremaud
gremaud@dali.math.ncsu.edu
In this talk, we will discuss a theory of a priori and a posteriori error
estimates for conservation laws obtained in collaboration with
Prof. B. Cockburn (U. of Minnesota).
More precisely, we will show how to use an approach introduced by
S.N. Kruskov and, later, by N.N Kuznetsov in the 70's, in order to
establish:
- a posteriori estimates for finite element methods for conservation laws,
and, using the "dual approach"
- a priori estimates for several families of algorithms.
Both results are significant in that they are the first, and to our
knowledge, the only ones of their kind (in the nonlinear case).
In particular, it is widely believed that error estimates for conservation
laws can only be obtained if strong regularity results for the approximate
solution can be proved (in many cases, this is not possible). Our "truly
a priori" result shows this to be incorrect.
The talk will focus more on the general ideas involved rather than on technical
details related to some particular algorithms.
|
