## New Approaches to Transport Problems

- March 1, 2010
- 2:30 p.m.
- LeConte 312

## Abstract

In this talk new concepts for the linear transport equation b•∇u + cu = ƒ are presented. To this end a functional analytic setting that allows control of the numerical errors in the L_{2}-norm is used. One possibility to make use of this setting is the usage of up-winded test functions. Because they are generally not members of the discrete spaces one needs to approximate them where it is important to take care that this approximation does not blow up the computational cost. Finally adaptive strategies are discussed. Because the right hand side is contained in a space that depends on the operator induced by the transport equation adaptive strategies to approximate the right hand side are crucial for these schemes.