Convergence of the point vortex method for the 2‐D euler equations

Jonathan Goodman; Thomas Y. Hou; John Lowengrub

doi:10.1002/cpa.3160430305

Convergence of the point vortex method for the 2‐D euler equations

Jonathan Goodman, Thomas Y. Hou, John Lowengrub

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove consistency, stability and convergence of the point vortex approximation to the 2‐D incompressible Euler equations with smooth solutions. We first show that the discretization error is second‐order accurate. Then we show that the method is stable in l_p norm. Consequently the method converges in l_p norm for all time. The convergence is also illustrated by a numerical experiment.

Original language	English (US)
Pages (from-to)	415-430
Number of pages	16
Journal	Communications on Pure and Applied Mathematics
Volume	43
Issue number	3
DOIs	https://doi.org/10.1002/cpa.3160430305
State	Published - Apr 1990

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.3160430305

Cite this

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title = "Convergence of the point vortex method for the 2‐D euler equations",

abstract = "We prove consistency, stability and convergence of the point vortex approximation to the 2‐D incompressible Euler equations with smooth solutions. We first show that the discretization error is second‐order accurate. Then we show that the method is stable in lp norm. Consequently the method converges in lp norm for all time. The convergence is also illustrated by a numerical experiment.",

author = "Jonathan Goodman and Hou, {Thomas Y.} and John Lowengrub",

year = "1990",

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AU - Hou, Thomas Y.

AU - Lowengrub, John

PY - 1990/4

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N2 - We prove consistency, stability and convergence of the point vortex approximation to the 2‐D incompressible Euler equations with smooth solutions. We first show that the discretization error is second‐order accurate. Then we show that the method is stable in lp norm. Consequently the method converges in lp norm for all time. The convergence is also illustrated by a numerical experiment.

AB - We prove consistency, stability and convergence of the point vortex approximation to the 2‐D incompressible Euler equations with smooth solutions. We first show that the discretization error is second‐order accurate. Then we show that the method is stable in lp norm. Consequently the method converges in lp norm for all time. The convergence is also illustrated by a numerical experiment.

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Convergence of the point vortex method for the 2‐D euler equations

Abstract

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