Liu, J-G; Xin, Z, *Convergence of point vortex method for 2-D vortex sheet*,
Math. Comp., vol. 70 no. 234
(2001),
pp. 565-606 [doi] .
**Abstract:**

*We give an elementary proof of the convergence of the point vortex method (PVM) to a classical weak solution for the two-dimensional incompressible Euler equations with initial vorticity being a finite Radon measure of distinguished sign and the initial velocity of locally bounded energy. This includes the important example of vortex sheets, which exhibits the classical Kelvin-Helmholtz instability. A surprise fact is that although the velocity fields generated by the point vortex method do not have bounded local kinetic energy, the limiting velocity field is shown to have a bounded local kinetic energy.*