418 IGPM418.pdf        March 2015
TITLE Stabilisation of hyperbolic conservation laws using conservative finite-volume schemes
AUTHORS Michael Herty
ABSTRACT We discuss numerical stabilisation of dynamics governed by nonlinear hyperbolic conservation laws through feedback boundary conditions. Using a discrete Lyapunov function we prove exponential decay of the discrete solution to first-order finite volume schemes in conservative form. Decay rates are established for a large class of finite volume schemes including the Lax-Friedrichs scheme. Theoretical results are accompanied by computational results.
KEYWORDS stabilisation, finite-volume schemes, Lyapunov methods, boundary control, hyperbolic conservation laws