  We present a simple discretization by radial basis functions for the Poisson
equation with Dirichlet boundary condition. A Lagrangian multiplier using
piecewise polynomials is used to accommodate the boundary condition. This
simplifies previous attempts to use radial basis functions in the interior
domain to approximate the solution and on the boundary to approximate the
multiplier, which technically requires that the mesh norm in the interior
domain is significantly smaller than that on the boundary. Numerical
experiments confirm theoretical results.
