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

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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

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Authors and Affiliations

  1. Lab. Jacques-Louis Lions, Université Pierre et Marie Curie, 175 Rue Chevaleret, Paris, 75013, France

    Olivier Bokanowski

  2. ENSTA, UMA, 32 Boulevard Victor, Paris Cedex 15, 75739, France

    Hasnaa Zidani

Authors
  1. Olivier Bokanowski
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  2. Hasnaa Zidani
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Correspondence to Olivier Bokanowski.

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AMS subject classifications. Primary 65M12, Secondary 58J47

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Bokanowski, O., Zidani, H. Anti-Dissipative Schemes for Advection and Application to Hamilton–Jacobi–Bellmann Equations. J Sci Comput 30, 1–33 (2007). https://doi.org/10.1007/s10915-005-9017-0

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  • DOI: https://doi.org/10.1007/s10915-005-9017-0

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