Year: 1985
Author: Chuan-Miao Chen
Journal of Computational Mathematics, Vol. 3 (1985), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1985-JCM-9601
Journal of Computational Mathematics, Vol. 3 (1985), Iss. 1 : pp. 1–7
Published online: 1985-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 7