Error Analysis of Approximate Operators for a Particle Method based on Voronoi Diagram
Numerical Analysis
2023-01-18 v2 Numerical Analysis
Abstract
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 example application of the main results of this paper.
Keywords
Cite
@article{arxiv.1904.02493,
title = {Error Analysis of Approximate Operators for a Particle Method based on Voronoi Diagram},
author = {Hajime Koba and Kazuki Sato},
journal= {arXiv preprint arXiv:1904.02493},
year = {2023}
}
Comments
1 figure. The authors changed the title of this paper, that is, we changed "Truncation Error Analysis of Approximate Operators for a Moving Particle Semi-Implicit Method" to "Error Analysis of Approximate Operators for a Particle Method based on Voronoi Diagram"