Abstract:  

Conservation laws are a widely used class of PDEs. One of them, the Aw-Rascle Zhang (ARZ) model, is applicable to the formulation of traffic flow which however has some unique features that lead to flaws in the basic finite volume methods for conservation laws: velocity overshoot/undershoot. This seminar mainly explains the fundamental crux of this problem. It extends from the theory of weak solutions to the specific performance of numerical formats.