On the Hughes model and numerical aspects

Diogo A. Gomes; Roberto Machado Velho

doi:10.1109/CDC.2016.7798683

On the Hughes model and numerical aspects

Diogo A. Gomes, Roberto Machado Velho

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.

Original language	English (US)
Title of host publication	2016 IEEE 55th Conference on Decision and Control (CDC)
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	2783-2788
Number of pages	6
ISBN (Print)	9781509018376
DOIs	https://doi.org/10.1109/CDC.2016.7798683
State	Published - Jan 5 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was partially supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering

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10.1109/CDC.2016.7798683

https://repository.kaust.edu.sa/bitstream/10754/622731/1/paper_Hughes_model_IEEE_version.pdf

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title = "On the Hughes model and numerical aspects",

abstract = "We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.",

author = "Gomes, {Diogo A.} and {Machado Velho}, Roberto",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was partially supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering",

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doi = "10.1109/CDC.2016.7798683",

language = "English (US)",

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AU - Gomes, Diogo A.

AU - Machado Velho, Roberto

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was partially supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering

PY - 2017/1/5

Y1 - 2017/1/5

N2 - We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.

AB - We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.

UR - http://hdl.handle.net/10754/622731

UR - http://ieeexplore.ieee.org/document/7798683/

UR - http://www.scopus.com/inward/record.url?scp=85010739226&partnerID=8YFLogxK

U2 - 10.1109/CDC.2016.7798683

DO - 10.1109/CDC.2016.7798683

M3 - Conference contribution

SN - 9781509018376

SP - 2783

EP - 2788

BT - 2016 IEEE 55th Conference on Decision and Control (CDC)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -

On the Hughes model and numerical aspects

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