Boundary stabilization of hyperbolic conservation laws using conservative finite volume schemes

摘要

We consider finite volume numerical schemes for stabilizing dynamics governed by scalar nonlinear hyperbolic conservation laws through feedback boundary conditions. Using a discrete Lyapunov function we prove the decay of the discrete solution given by first-order finite volume schemes in conservative form to a desired stationary state up to the order of the time step. Theoretical results are accompanied by a computational example.