Error analysis of approximate operators for a particle method based on Voronoi diagram-Reference-Cited by-同舟云学术

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

Published:2023-02-28 Issue:4 Volume:43 Page:267-283
ISSN:0174-4747
Container-title:Analysis
language:en
Short-container-title:

Author:

Koba Hajime¹^ORCID,Sato Kazuki¹

Affiliation:

1. Graduate School of Engineering Science , Osaka University , 1-3 Machikaneyamacho , Toyonaka , Osaka, 560-8531 , Japan

Abstract

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 exemplary application of the main results of this paper.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anly-2022-1104/pdf

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