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IGPM418.pdf March 2015 
TITLE 
Stabilisation of hyperbolic conservation laws using conservative finitevolume 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 firstorder finite volume schemes in conservative form. Decay rates are established for a large class of finite volume schemes including
the LaxFriedrichs scheme. Theoretical results are accompanied by computational results.

KEYWORDS 
stabilisation, finitevolume schemes, Lyapunov methods, boundary control, hyperbolic conservation laws 