Truncation error estimates of approximate differential operators of a particle method based on the Voronoi decomposition

Abstract

Truncation errors are considered for approximate differential operators with a class of particle methods. Introducing sufficient conditions for the weight function and a regularity of the family of discrete parameters leads to truncation error estimates of approximate gradient and Laplace operators with a particle method based on the Voronoi decomposition. Moreover, some numerical results agree well with theoretical ones.