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

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.