Numerical Approximation of the Critical Value of Eikonal Hamilton-Jacobi Equations on Networks
arXiv:2502.20993 · doi:10.1007/s00245-026-10449-5
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.
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