Error analysis of approximate operators for a particle method based on Voronoi diagram

The final publication is available at https://doi.org/10.1515/anly-2022-1104.
This paper considers several approximate operators used in a particle method based on a Voronoi diagram. We introduce and study our approximate operators on gradient and Laplace operators. We derive error estimates for these approximate operators by applying our weight functions. The key idea of deriving our error estimates is to divide the integration region into a ring-shaped area and some areas. In the appendix, we give an exemplary application of the main results of this paper.