@Article{JCM-3-1, author = {Chen , Chuan-Miao}, 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 = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9601.html} }