Convergent finite difference schemes for stochastic transport equations

09/05/2023

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by   Ulrik S. Fjordholm, et al.

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We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish L^2 stability and convergence of the difference approximations under conditions that are less strict than those required for deterministic transport equations. The L^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.