This paper considers several approximate operators used in a particle method
based on a Voronoi diagram. Under some assumptions on a weight function, we
derive truncation error estimates for our approximate gradient and Laplace
operators. Our results show that our approximate gradient and Laplace operators
tend to the usual gradient and Laplace operators when the ratio (the radius of
the interaction area/the radius of a Voronoi cell) is sufficiently large. The
key idea of our approach is to divide the integration region into two
ring-shaped areas.Comment: 2 figure