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

Jonathan Goodman, Thomas Y. Hou, John Lowengrub

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)415-430
Number of pages16
JournalCommunications on Pure and Applied Mathematics
Volume43
Issue number3
DOIs
StatePublished - 1990

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Vortex Method
Point Vortex
Lp-norm
Euler equations
Euler Equations
Vortex flow
Incompressible Euler Equations
Discretization Error
Stability and Convergence
Smooth Solution
Experiments
Numerical Experiment
Converge
Approximation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Convergence of the point vortex method for the 2‐D euler equations. / Goodman, Jonathan; Hou, Thomas Y.; Lowengrub, John.

In: Communications on Pure and Applied Mathematics, Vol. 43, No. 3, 1990, p. 415-430.

Research output: Contribution to journalArticle

Goodman, Jonathan ; Hou, Thomas Y. ; Lowengrub, John. / Convergence of the point vortex method for the 2‐D euler equations. In: Communications on Pure and Applied Mathematics. 1990 ; Vol. 43, No. 3. pp. 415-430.
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