Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms

Unique solvability and stability analysis is conducted for a generalized particle method for a Poisson equation with a source term given in divergence form. The general- ized particle method is a numerical method for partial differential equations categorized into meshfree particle methods and generally indicates conventional particle methods such as smoothed particle hydrodynamics and moving particle semi-implicit methods. Unique solv- ability is derived for the generalized particle method for the Poisson equation by introducing a connectivity condition for particle distributions. Moreover, stability is obtained for the discretized Poisson equation by introducing discrete Sobolev norms and a semi-regularity condition of a family of discrete parameters.