Section: New Results

Hyperbolic Problems, Conservation laws and Gas Dynamics

The convergence analysis of numerical schemes for conservation laws with unstructured meshes with an original proof based on probabilistic argument is a striking result due to F. Lagoutière with F. Delarue, [52] . More generally, we refer to [53] for an overview of F. Lagoutière's works.

The analysis of the stability of compressible vortex sheets has been carried out in [49] ,[13] by J.-F. Coulombel and P. Secchi. J.-F. Coulombel also studies the stability of finite difference approximation of hyperbolic problems with boundary conditions [10] , [28] , [11] . He generalizes and simplifies previous results by Gustaffson-Kreiss-Sundstrom. Part of this work is a new collaboration with A. Gloria. In a collaboration with O. Guès, J.-F. Coulombel has obtained a detailed description for the propagation of high frequency signals in hyperbolic systems, and their reflection on the boundary [29] , [48] . A synthetic survey of these results can be found on [47] ,[23] .