Published Paper

Inserted: 27 jun 2026

Journal: SIAM Journal on Numerical Analysis
Volume: 64
Number: 3
Pages: 29
Year: 2026
Doi: https://doi.org/10.1137/25M1760350

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: one-sided Lipschitz condition, semi-Lagrangian schemes, viscous transport equation, measure-valued solution