|Preprint-No.:||< 418 >||Published in:||March 2015||PDF-File:||IGPM418.pdf|
|Title:||Stabilisation of hyperbolic conservation laws using conservative finite–volume schemes|
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|