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Networks and Heterogeneous Media

2013, Volume 8, Issue 3: 685-705. doi: 10.3934/nhm.2013.8.685
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Numerical discretization of Hamilton--Jacobi equations on networks

  • 1.
    University of Mannheim, School of Business Informatics and Mathematics, A5-6, 68131 Mannheim
  • 2.
    RWTH Aachen University, IGPM, Templergraben 55, 52056 Aachen
  • Received: 01 November 2012 Revised: 01 June 2013

  • Primary: 90B20, 35L50; Secondary: 35F21.

  • We discuss a numerical discretization of Hamilton--Jacobi equations on networks. The latter arise for example as reformulation of the Lighthill--Whitham--Richards traffic flow model. We present coupling conditions for the Hamilton--Jacobi equations and derive a suitable numerical algorithm. Numerical computations of travel times in a round-about are given.

    Citation: Simone Göttlich, Ute Ziegler, Michael Herty. Numerical discretization of Hamilton--Jacobi equations on networks[J]. Networks and Heterogeneous Media, 2013, 8(3): 685-705. doi: 10.3934/nhm.2013.8.685

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  • We discuss a numerical discretization of Hamilton--Jacobi equations on networks. The latter arise for example as reformulation of the Lighthill--Whitham--Richards traffic flow model. We present coupling conditions for the Hamilton--Jacobi equations and derive a suitable numerical algorithm. Numerical computations of travel times in a round-about are given.


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