CONVERGENT FINITE DIFFERENCE SCHEMES FOR STOCHASTIC TRANSPORT EQUATIONS

被引：0

作者：

Fjordholm, Ulrik S. ^{[1
]}

Karlsen, Kenneth H. ^{[1
]}

Pang, Peter H. C. ^{[1
]}

机构：

[1] Univ Oslo, Dept Math, Oslo, Norway

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2025年 / 63卷 / 01期

关键词：

stochastic transport equation; gradient noise; finite difference scheme; regularization by noise; stability; convergence; DISCONTINUOUS GALERKIN METHOD; SCALAR CONSERVATION-LAWS; VOLUME SCHEME; RENORMALIZED SOLUTIONS; APPROXIMATIONS;

D O I：

10.1137/23M159946X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish L2 stability and convergence of the difference approximations under conditions that are less strict than those required for deterministic transport equations. The L2 estimate, crucial for the analysis, is obtained through a discrete duality argument and a comprehensive examination of a class of backward parabolic difference schemes.

引用

页码：149 / 192

页数：44

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