CONVERGENT FINITE DIFFERENCE SCHEMES FOR STOCHASTIC TRANSPORT EQUATIONS

Ulrik S. Fjordholm; Kenneth H. Karlsen; Peter H.C. Pang

doi:10.1137/23M159946X

CONVERGENT FINITE DIFFERENCE SCHEMES FOR STOCHASTIC TRANSPORT EQUATIONS

Ulrik S. Fjordholm, Kenneth H. Karlsen, Peter H.C. Pang

Research output: Journal Publication › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	149-192
Number of pages	44
Journal	SIAM Journal on Numerical Analysis
Volume	63
Issue number	1
DOIs	https://doi.org/10.1137/23M159946X
Publication status	Published - 2025
Externally published	Yes

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1137/23M159946X

Cite this

@article{1815f79c166946a697bd33b1be290905,

title = "CONVERGENT FINITE DIFFERENCE SCHEMES FOR STOCHASTIC TRANSPORT EQUATIONS",

abstract = "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.",

author = "Fjordholm, \{Ulrik S.\} and Karlsen, \{Kenneth H.\} and Pang, \{Peter H.C.\}",

note = "Publisher Copyright: {\textcopyright} 2025 Society for Industrial and Applied Mathamatics.",

year = "2025",

doi = "10.1137/23M159946X",

language = "English",

volume = "63",

pages = "149--192",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - CONVERGENT FINITE DIFFERENCE SCHEMES FOR STOCHASTIC TRANSPORT EQUATIONS

AU - Fjordholm, Ulrik S.

AU - Karlsen, Kenneth H.

AU - Pang, Peter H.C.

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85216926863

U2 - 10.1137/23M159946X

DO - 10.1137/23M159946X

M3 - Article

AN - SCOPUS:85216926863

SN - 0036-1429

VL - 63

SP - 149

EP - 192

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 1

ER -

CONVERGENT FINITE DIFFERENCE SCHEMES FOR STOCHASTIC TRANSPORT EQUATIONS

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this