Error Analysis of Approximate Operators for a Particle Method based on Voronoi Diagram

Abstract

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.2010 Mathematics Subject Classification. 33F05.