  We prove the convergence of meshfree method for solving the elliptic
Monge-Ampere equation with Dirichlet boundary on the bounded domain. L2 error
is obtained based on the kernel-based trial spaces generated by the compactly
supported radial basis functions. We obtain the convergence result when the
testing discretization is finer than the trial discretization. The convergence
rate depend on the regularity of the solution, the smoothness of the computing
domain, and the approximation of scaled kernel-based spaces. The presented
convergence theory covers a wide range of kernel-based trial spaces including
stationary approximation and non-stationary approximation. An extension to
non-Dirichlet boundary condition is in a forthcoming paper.
