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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Convergence of the random vortex method in two dimensions


Author: Ding-Gwo Long
Journal: J. Amer. Math. Soc. 1 (1988), 779-804
MSC: Primary 65M10; Secondary 65M15, 76-08, 76C05, 76D05
MathSciNet review: 958446
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Abstract: A theoretical framework for analyzing the random vortex method is presented. It extends and modifies the analysis of the inviscid vortex method in a natural and unified manner.

The rate of convergence of the random vortex method in two dimensions is obtained by analyzing the consistency error and justifying the stability estimate. The sampling error introduced by the random motions of finitely many vortices is the dominant component of the consistency error in terms of order. It is estimated by applying Bennett's inequality.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0894-0347-1988-0958446-1
PII: S 0894-0347(1988)0958446-1
Article copyright: © Copyright 1988 American Mathematical Society