East Asian J. Appl. Math., 15 (2025), pp. 650-668.
Published online: 2025-06
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2024-146.021224}, url = {http://global-sci.org/intro/article_detail/eajam/24159.html} }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.