Volume 14, Issue 4
Optimal Interior and Local Error Estimates of a Recovered Gradient of Linear Elements on Nonuniform Triangulations

I. Hlavavcek & M. Kvrivzek

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J. Comp. Math., 14 (1996), pp. 345-362

Published online: 1996-08

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  • Abstract

We examine a simple averaging formula for the gradient of linear finite elements in $R^d$ whose interpolation order in the $L^q$-norm is $\Cal O(h^2)$ for $d<2q$ and nonuniform triangulations. For elliptic problems in $R^2$ we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. Local error estimates up to a regular part of the boundary and the effect of numerical integration are also investigated.

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@Article{JCM-14-345, author = {}, title = {Optimal Interior and Local Error Estimates of a Recovered Gradient of Linear Elements on Nonuniform Triangulations}, journal = {Journal of Computational Mathematics}, year = {1996}, volume = {14}, number = {4}, pages = {345--362}, abstract = { We examine a simple averaging formula for the gradient of linear finite elements in $R^d$ whose interpolation order in the $L^q$-norm is $\Cal O(h^2)$ for $d<2q$ and nonuniform triangulations. For elliptic problems in $R^2$ we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. Local error estimates up to a regular part of the boundary and the effect of numerical integration are also investigated. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9244.html} }
TY - JOUR T1 - Optimal Interior and Local Error Estimates of a Recovered Gradient of Linear Elements on Nonuniform Triangulations JO - Journal of Computational Mathematics VL - 4 SP - 345 EP - 362 PY - 1996 DA - 1996/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9244.html KW - AB - We examine a simple averaging formula for the gradient of linear finite elements in $R^d$ whose interpolation order in the $L^q$-norm is $\Cal O(h^2)$ for $d<2q$ and nonuniform triangulations. For elliptic problems in $R^2$ we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. Local error estimates up to a regular part of the boundary and the effect of numerical integration are also investigated.
I. Hlavavcek & M. Kvrivzek. (1970). Optimal Interior and Local Error Estimates of a Recovered Gradient of Linear Elements on Nonuniform Triangulations. Journal of Computational Mathematics. 14 (4). 345-362. doi:
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