$W^{1,∞}$-Interior Estimates for Finite Element Method on Regular Mesh

$W^{1,∞}$-Interior Estimates for Finite Element Method on Regular Mesh

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

Keywords:   

Author Details

Chuan-Miao Chen