Year: 2025
Author: Wenming He, Mingxiang Deng, Yongping Feng, Xiaofei Guan
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 3 : pp. 650–668
Abstract
A state of the art technology is employed to investigate the local ultraconvergence properties of a quadratic rectangular element for the Poisson equation. The proposed method combine advantages of a novel interpolation postprocessing operator $\overline{P}^6_{6h,m} R^∗_h ,$ the Richardson extrapolation technique, and properties of a discrete Green’s function. The local ultraconvergence of the post-processed gradient of the finite element solution is derived with the order $\mathcal{O}(h^6 |{\rm ln}h|^2).$ A numerical example shows a good agreement with the theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2024-146.021224
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 3 : pp. 650–668
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Ultraconvergence quadratic rectangular element integral identity local symmetric interpolation postprocessing.