Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Abstract
We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show.
Cite
@article{arxiv.math/0403517,
title = {Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle},
author = {Folkmar Bornemann and Christian Rasch},
journal= {arXiv preprint arXiv:math/0403517},
year = {2025}
}
Comments
19 pages