Error Estimate for a Semi-Lagrangian Scheme for Hamilton-Jacobi Equations on Networks

2024/11/04 by Carlini, Elisabetta, Coscetti, Valentina, Pozza, Marco
#35R02 #49L25 #65M12 #65M15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2411.02356

Abstract

We examine the numerical approximation of time-dependent Hamilton-Jacobi equations on networks, providing a convergence error estimate for the semi-Lagrangian scheme introduced in (Carlini and Siconolfi, 2023), where convergence was proven without an error estimate. We derive a convergence error estimate of order one-half. This is achieved showing the equivalence between two definitions of solutions to this problem proposed in (Imbert and Monneau, 2017) and (Siconolfi, 2022), a result of independent interest, and applying a general convergence result from (Carlini, Festa and Forcadel, 2020).

Related

• Numerical Analysis of time-dependent Hamilton-Jacobi Equations on Networks
• A semi-Lagrangian scheme for Hamilton-Jacobi equations on networks with application to traffic flow models
• An approximation scheme for an Hamilton-Jacobi equation defined on a network
• Numerical Approximation of the Critical Value of Eikonal Hamilton-Jacobi Equations on Networks
• A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applications