Numerical discretization of Hamilton--Jacobi equations on networks

Simone Göttlich; Ute Ziegler; Michael Herty; Simone Göttlich; Ute Ziegler; Michael Herty

doi:10.3934/nhm.2013.8.685

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.
- Networks,
- traffic flow,
- Hamilton-Jacobi Equations
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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Abstract

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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