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,  . More generally, we refer to  for an overview of F. Lagoutière's works.
The analysis of the stability of compressible vortex sheets has been carried out in  , by J.-F. Coulombel and P. Secchi. J.-F. Coulombel also studies the stability of finite difference approximation of hyperbolic problems with boundary conditions  ,  ,  . 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  ,  . A synthetic survey of these results can be found on  , .