Numerical Approximation of the Critical Value of Eikonal Hamilton-Jacobi Equations on Networks
Numerical Analysis
2025-10-03 v2 Numerical Analysis
Analysis of PDEs
Abstract
The critical value of an eikonal equation is the unique value of a parameter for which the equation admits solutions and is deeply related to the effective Hamiltonian of a corresponding homogenization problem. We study approximation strategies for the critical value of eikonal equations posed on networks. They are based on the large time behavior of corresponding time-dependent Hamilton-Jacobi equations. We provide error estimates and some numerical tests, showing the performance and the convergence properties of the proposed algorithms.
Keywords
Cite
@article{arxiv.2502.20993,
title = {Numerical Approximation of the Critical Value of Eikonal Hamilton-Jacobi Equations on Networks},
author = {Valentina Coscetti and Marco Pozza},
journal= {arXiv preprint arXiv:2502.20993},
year = {2025}
}