Year: 2021
Author: Weiwei Zhang, Long Hu, Zongze Yang, Yufeng Nie
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 3 : pp. 324–338
Abstract
In the natural element method (NEM), the Laplace interpolation error estimate on
convex planar polygons is proved in this study. The proof is based on bounding gradients of the
Laplace interpolation for convex polygons which satisfy certain geometric requirements, and has
been divided into several parts that each part is bounded by a constant. Under the given geometric
assumptions, the optimal convergence estimate is obtained. This work provides the mathematical
analysis theory of the NEM. Some numerical examples are selected to verify our theoretical result.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-18722
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 3 : pp. 324–338
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Natural element method geometric constraints Laplace interpolation error estimate.