Archive for Rational Mechanics and Analysis

, Volume 167, Issue 1, pp 1–81

BV Solutions of the Semidiscrete Upwind Scheme

  • Stefano Bianchini

DOI: 10.1007/s00205-002-0237-2

Cite this article as:
Bianchini, S. Arch. Rational Mech. Anal. (2003) 167: 1. doi:10.1007/s00205-002-0237-2

We consider the semidiscrete upwind scheme
$$$$
We prove that if the initial data ū of (1) has small total variation, then the solution uɛ(t) has uniformly bounded BV norm, independent of t, ɛ. Moreover by studying the equation for a perturbation of (1) we prove the Lipschitz-continuous dependence of uɛ(t) on the initial data. Using a technique similar to the vanishing-viscosity case, we show that as ɛ→0 the solution uɛ(t) converges to a weak solution of the corresponding hyperbolic system,
$$$$

Moreover this weak solution coincides with the trajectory of a Riemann semigroup, which is uniquely determined by the extension of Liu's Riemann solver to general hyperbolic systems.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Stefano Bianchini
    • 1
  1. 1.Istituto per le Applicazioni del Calcolo ``M. Picone'' - CNR, Viale del Policlinico 137, 00161 Roma (ITALY) e-mail: bianchin@iac.rm.cnr.itIT