Well-Posedness and Convergence of a Finite Volume Method for Conservation Laws on Networks

DOI10.1137/21M145001XOpenAlexW4221059541MaRDI QIDQ3390686

Markus Musch, Nils Henrik Risebro, Ulrik Skre Fjordholm

Publication date: 25 March 2022

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/21m145001x

zbMATH Keywords

finite volume methodsnetworkshyperbolic conservation laws

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Numerical analysis (65-XX) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (3)

Partial differential equations on hypergraphs and networks of surfaces: Derivation and hybrid discretizations ⋮ On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods ⋮ Microscopic derivation of a traffic flow model with a bifurcation

Cites Work

• Unnamed Item
• Unnamed Item
• Global solution of the Cauchy problem for a class of 2x2 nonstrictly hyperbolic conservation laws
• A review of conservation laws on networks
• Well-posedness for vanishing viscosity solutions of scalar conservation laws on a network
• Well-posedness theory for nonlinear scalar conservation laws on networks
• Vanishing viscosity on a star-shaped graph under general transmission conditions at the node
• Flows on networks: recent results and perspectives
• Vanishing viscosity for traffic on networks with degenerate diffusivity
• Vanishing Viscosity for Traffic on Networks
• Some Relations Between Nonexpansive and Order Preserving Mappings
• Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes
• Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux
• A Difference Scheme for Conservation Laws with a Discontinuous Flux: The Nonconvex Case
• Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies
• Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient
• A Mathematical Model of Traffic Flow on a Network of Unidirectional Roads
• Traffic Flow on a Road Network
• Shock Waves on the Highway
• On kinematic waves II. A theory of traffic flow on long crowded roads

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