Alberto Bressan
Penn State University
The talk will discuss the stability and convergence of finite difference schemes for hyperbolic systems of conservation laws. If in the Glimm scheme the restartings are performed by averaging (instead of random sampling), one obtains a simple numerical scheme for the construction of approximate solutions. We will show that, even for small initial data, this method can produce an arbitrarily large amount of oscillations. This instability is due to resonances which occur when the speed of a shock is close to rational, compared with the grid size.