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 generalized 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 solvability is derived for the generalized particle method for the...