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Convergence of the point vortex method for the 2‐D euler equations
Author(s) -
Goodman Jonathan,
Hou Thomas Y.,
Lowengrub John
Publication year - 1990
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160430305
Subject(s) - mathematics , discretization , backward euler method , norm (philosophy) , convergence (economics) , euler equations , compressibility , mathematical analysis , vortex , euler method , convergence tests , euler's formula , rate of convergence , physics , channel (broadcasting) , electrical engineering , engineering , political science , law , economics , thermodynamics , economic growth
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.