TY - JOUR
T1 - Local Ultraconvergence of Quadratic Rectangular Element
AU - He , Wenming
AU - Deng , Mingxiang
AU - Feng , Yongping
AU - Guan , Xiaofei
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 650
EP - 668
PY - 2025
DA - 2025/06
SN - 15
DO - http://doi.org/10.4208/eajam.2024-146.021224
UR - https://global-sci.org/intro/article_detail/eajam/24159.html
KW - Ultraconvergence, quadratic rectangular element, integral identity, local symmetric, interpolation postprocessing.
AB - <p style="text-align: justify;">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.</p>