Numerical discretization of Hamilton--Jacobi equations on networks

Simone Göttlich; Ute Ziegler; Michael Herty

doi:10.3934/nhm.2013.8.685

Article Contents

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: October 31, 2012

Revised: May 31, 2013

Published: August 2013

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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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Mathematics Subject Classification: Primary: 90B20, 35L50; Secondary: 35F21.

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