Approximation of Viscous Transport and Conservative Equations with One Sided Lipschitz Velocity Fields
Abstract
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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- SIAM Journal on Numerical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 64
- Issue
- 3
- Pages
- 1043–1071
- Publication date
- 23 June 2026
- Language
- EN