Convergent finite difference schemes for stochastic transport equations
Numerical Analysis
2025-01-27 v4 Numerical Analysis
Analysis of PDEs
Abstract
We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish stability and convergence of the difference approximations under conditions that are less strict than those required for deterministic transport equations. The estimate, crucial for the analysis, is obtained through a discrete duality argument and a comprehensive examination of a class of backward parabolic difference schemes.
Cite
@article{arxiv.2309.02208,
title = {Convergent finite difference schemes for stochastic transport equations},
author = {Ulrik S. Fjordholm and Kenneth H. Karlsen and Peter H. C. Pang},
journal= {arXiv preprint arXiv:2309.02208},
year = {2025}
}
Comments
42 pages; minor amendments and typos corrected