Nonlinear Stability of Discrete Shocks for Systems of Conservation Laws

@inproceedings{Liu2004NonlinearSO,
  title={Nonlinear Stability of Discrete Shocks for Systems of Conservation Laws},
  author={Guo Liu and T Xin},
  year={2004}
}
In this paper we study the asymptotic nonlinear stability of discrete shocks for the Lax-Friedrichs scheme for approximating general m • systems of nonlinear hyperbolic conservation laws. It is shown that weak single discrete shocks for such a scheme are nonlinearly stable in the LP-norm for all p __> 1, provided that the sums of the initial perturbations equal zero. These results should shed light on the convergence of the numerical solution constructed by the Lax-Friedrichs scheme for the… CONTINUE READING

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