An approximation scheme for a Hamilton-Jacobi equation defined on a network

DOI10.1016/j.apnum.2013.05.003zbMath1302.65210arXiv1105.5725OpenAlexW1980008163MaRDI QIDQ465049

Adriano Festa, Dirk Schieborn, Fabio Camilli

Publication date: 31 October 2014

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5725

zbMATH Keywords

networkstabilityconvergencenumerical exampleHamilton-Jacobi equationviscosity solutionfinite elementsemidiscretization

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Hamilton-Jacobi equations (35F21)

Related Items (13)

Discontinuous solutions of Hamilton-Jacobi equations on networks ⋮ Morphological PDE and Dilation/Erosion Semigroups on Length Spaces ⋮ Approximation of the Value Function for Optimal Control Problems on Stratified Domains ⋮ Navigation system-based routing strategies in traffic flows on networks ⋮ Error estimates for a finite difference scheme associated with Hamilton-Jacobi equations on a junction ⋮ Viscosity solutions of eikonal equations on topological networks ⋮ Two numerical approaches to stationary mean-field games ⋮ A flame propagation model on a network with application to a blocking problem ⋮ A Semi-Lagrangian Scheme for Hamilton--Jacobi--Bellman Equations on Networks ⋮ A discrete Hughes model for pedestrian flow on graphs ⋮ One-dimensional forward-forward mean-field games ⋮ A convergent scheme for Hamilton-Jacobi equations on a junction: application to traffic ⋮ Eikonal equations in metric spaces

Cites Work

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• Differential equations on networks (geometric graphs)
• Viscosity solutions of eikonal equations on topological networks
• Maximal subsolutions for a class of degenerate Hamilton-Jacobi problems
• A Hamilton-Jacobi approach to junction problems and application to traffic flows
• Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

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