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Journal of Scientific Computing

, Volume 30, Issue 1, pp 1–33 | Cite as

Anti-Dissipative Schemes for Advection and Application to Hamilton–Jacobi–Bellmann Equations

  • Olivier Bokanowski
  • Hasnaa Zidani
Article

Abstract

We propose two new antidiffusive schemes for advection (or linear transport), one of them being a mixture of Roe’s Super-Bee scheme and of the “Ultra-Bee” scheme. We show how to apply these schemes to treat time-dependent first order Hamilton–Jacobi–Bellman equations with discontinuous initial data, possibly infinitely-valued. Numerical tests are proposed, in one and two space dimensions, in order to validate the methods

Keywords

Advection equation antidiffusive scheme Ultra-Bee limiter Super-Bee limiter Hamilton–Jacobi–Bellman equation 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Lab. Jacques-Louis LionsUniversité Pierre et Marie CurieParisFrance
  2. 2.ENSTA, UMAParis Cedex 15France

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