Approximation of viscous transport and conservative equations with one sided Lipschitz velocity fields
Numerical Analysis
2025-05-15 v1 Numerical Analysis
Abstract
The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the convergence of the schemes, we exploit the characterization of the solution for these equations expressed in terms of measurable time-dependent viscosity solution and, respectively, duality solution. We supplement our theoretical analysis with various numerical examples to illustrate the features of the schemes.
Keywords
Cite
@article{arxiv.2505.08970,
title = {Approximation of viscous transport and conservative equations with one sided Lipschitz velocity fields},
author = {Fabio Camilli and Adriano Festa and Luciano Marzufero},
journal= {arXiv preprint arXiv:2505.08970},
year = {2025}
}