English

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 L2L^2 stability and convergence of the difference approximations under conditions that are less strict than those required for deterministic transport equations. The L2L^2 estimate, crucial for the analysis, is obtained through a discrete duality argument and a comprehensive examination of a class of backward parabolic difference schemes.

Keywords

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

R2 v1 2026-06-28T12:13:05.875Z