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