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, [56] . More generally, we refer to [59] for an overview of F. Lagoutière's works.

J.-F. Coulombel has studied the stability of finite difference approximations of hyperbolic systems with boundary conditions. This series of works, part of which is a collaboration with A. Gloria, generalizes and simplifies previous results by Gustafsson, Kreiss, Tadmor, Wu and others. In collaboration with O. Guès and M. Williams, J.-F. Coulombel has also studied the justification of geometric optics for hyperbolic boundary value problems. The results describe the reflection of highly oscillating wave trains on a boundary. Eventually, J.-F. Coulombel has studied with S. Benzoni and N. Tzvetkov well-posedness issues for some nonlocal versions of Burgers equation.