Numerische Mathematik

, Volume 115, Issue 1, pp 1–44 | Cite as

Convergence of a non-monotone scheme for Hamilton–Jacobi–Bellman equations with discontinous initial data

Article

Abstract

We prove the convergence of a non-monotonous scheme for a one-dimensional first order Hamilton–Jacobi–Bellman equation of the form v t + max α (f(x, α)v x ) = 0, v(0, x) = v 0(x). The scheme is related to the HJB-UltraBee scheme suggested in Bokanowski and Zidani (J Sci Comput 30(1):1–33, 2007). We show for general discontinuous initial data a first-order convergence of the scheme, in L 1-norm, towards the viscosity solution. We also illustrate the non-diffusive behavior of the scheme on several numerical examples.

Mathematics Subject Classification (2000)

65M12 65M15 35F25 35F99 49L25 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Olivier Bokanowski
    • 1
    • 2
  • Nadia Megdich
    • 3
    • 4
  • Hasnaa Zidani
    • 4
  1. 1.Laboratoire J.-L. LionsUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.UFR de Mathématiques, Site ChevaleretUniversité Paris-DiderotParis CedexFrance
  3. 3.ISECS, Institut supérieur d’électronique et communication de SfaxSfaxTunisia
  4. 4.Project Commands ENSTA, Inria Saclay, CMAP, UMAParis Cedex 15France

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