Stability of a generalized particle method for a Poisson equation by discrete Sobolev norms

Numerical analysis is conducted for a generalized particle method for a Poisson equation. Unique solvability is derived for the discretized Poisson equation by introducing a connectivity condition for particle distributions. Moreover, by introducing discrete Sobolev norms and a semi-regularity of a family of discrete parameters, stability is obtained for the discretized Poisson equation based on the norms.