Numerical scheme for a class of linear dispersive systems with boundaries conditions

This talk concerns the numerical approximations of a class of linear dispersive Initial Boundary Value Problems (IBVP) which describe the wave propagation in dispersive media. The considered class of IBVP is defined by assumptions on the symmetrization and on the boundary conditions. Under these assumptions, a reformulation of the IBVP with non-local conservation laws will be established. This reformulation will lead to H^1 estimates for the solutions of the dispersive IBVP. A numerical strategy will be proposed to enforce a fully discrete version of such estimates and numerical experiments will be done to assess its relevancy.