@Article{JCM-3-1,
author = {Chuan-Miao, Chen},
title = {$W^{1,∞}$-Interior Estimates for Finite Element Method on Regular Mesh},
journal = {Journal of Computational Mathematics},
year = {1985},
volume = {3},
number = {1},
pages = {1--7},
abstract = {<p style="text-align: justify;">For a large class of piecewise polynomial subspaces $S^h$ defined on the regular mesh, $W^{1,∞}$-interior estimate $\|u_h\|_{1,∞,Ω_0}$ ≤ $c\|u_h\|_{-s,Ω_1}$, $u_h\in S^h{Ω_1}$ satisfying the interior Ritz equation is proved. For the finite element approximation $u_h$ (of degree $r-1$) to $u$, we have $W^{1,∞}$-interior error estimate $\|u-u_h\|_{1,∞,Ω_0}$)≤$ch^{r-1} (\|u\|_{r,∞,Ω_1}+\|u\|_{1,Ω}$). If the triangulation is strongly regular in $Ω_1$ and $r=2$ we obtain $W^{1,∞}$-interior superconvergence.</p>},
issn = {1991-7139},
doi = {https://doi.org/1985-JCM-9601},
url = {https://global-sci.com/article/86230/w1-interior-estimates-for-finite-element-method-on-regular-mesh}
}