Journal
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
Volume 55, Issue 2, Pages 689-711Publisher
EDP SCIENCES S A
DOI: 10.1051/m2an/2021006
Keywords
Traffic flow; macroscopic models; non-local model; homogenization; viscosity solutions; Hamilton– Jacobi equations
Categories
Funding
- European Union
- European regional development fund (ERDF) [18P03390/18E01750/18P02733]
- Normandie Regional Council via the M2SiNUM project
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This work introduces a non-local Hamilton-Jacobi model for traffic flow and proves the existence and uniqueness of its solution, as well as a numerical scheme with estimated error. It also presents some numerical illustrations.
In this work, we propose a non-local Hamilton-Jacobi model for traffic flow and we prove the existence and uniqueness of the solution of this model. This model is justified as the limit of a rescaled microscopic model. We also propose a numerical scheme and we prove an estimate error between the continuous solution of this problem and the numerical one. Finally, we provide some numerical illustrations.
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