Finite element derivative interpolation recovery technique and superconvergence

Tie Zhu Zhang; Shu Hua Zhang

Applications of Mathematics (2011)

  • Volume: 56, Issue: 6, page 513-531
  • ISSN: 0862-7940

Abstract

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A new finite element derivative recovery technique is proposed by using the polynomial interpolation method. We show that the recovered derivatives possess superconvergence on the recovery domain and ultraconvergence at the interior mesh points for finite element approximations to elliptic boundary problems. Compared with the well-known Z-Z patch recovery technique, the advantage of our method is that it gives an explicit recovery formula and possesses the ultraconvergence for the odd-order finite elements. Finally, some numerical examples are presented to illustrate the theoretical analysis.

How to cite

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Zhang, Tie Zhu, and Zhang, Shu Hua. "Finite element derivative interpolation recovery technique and superconvergence." Applications of Mathematics 56.6 (2011): 513-531. <http://eudml.org/doc/196642>.

@article{Zhang2011,
abstract = {A new finite element derivative recovery technique is proposed by using the polynomial interpolation method. We show that the recovered derivatives possess superconvergence on the recovery domain and ultraconvergence at the interior mesh points for finite element approximations to elliptic boundary problems. Compared with the well-known Z-Z patch recovery technique, the advantage of our method is that it gives an explicit recovery formula and possesses the ultraconvergence for the odd-order finite elements. Finally, some numerical examples are presented to illustrate the theoretical analysis.},
author = {Zhang, Tie Zhu, Zhang, Shu Hua},
journal = {Applications of Mathematics},
keywords = {finite element method; derivative recovery technique; superconvergence and ultraconvergence; elliptic boundary problems; numerical examples; finite element method; derivative recovery technique; superconvergence; ultraconvergence; elliptic boundary problems; numerical examples},
language = {eng},
number = {6},
pages = {513-531},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite element derivative interpolation recovery technique and superconvergence},
url = {http://eudml.org/doc/196642},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Zhang, Tie Zhu
AU - Zhang, Shu Hua
TI - Finite element derivative interpolation recovery technique and superconvergence
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 6
SP - 513
EP - 531
AB - A new finite element derivative recovery technique is proposed by using the polynomial interpolation method. We show that the recovered derivatives possess superconvergence on the recovery domain and ultraconvergence at the interior mesh points for finite element approximations to elliptic boundary problems. Compared with the well-known Z-Z patch recovery technique, the advantage of our method is that it gives an explicit recovery formula and possesses the ultraconvergence for the odd-order finite elements. Finally, some numerical examples are presented to illustrate the theoretical analysis.
LA - eng
KW - finite element method; derivative recovery technique; superconvergence and ultraconvergence; elliptic boundary problems; numerical examples; finite element method; derivative recovery technique; superconvergence; ultraconvergence; elliptic boundary problems; numerical examples
UR - http://eudml.org/doc/196642
ER -

References

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  14. Zhang, T., Lin, Y. P., Tait, R. J., The derivative patch interpolation recovery technique for finite element approximations, J. Comput. Math. 22 (2004), 113-122. (2004) MR2027918
  15. Zhang, T., Li, C. J., Nie, Y. Y., Derivative superconvergence of linear finite elements by recovery techniques, Dyn. Contin. Discrete Impuls. Syst., Ser. A 11 (2004), 853-862. (2004) Zbl1059.65096MR2077127
  16. Zhang, T., Finite Element Methods for Evolutionary Integro-Differential Equations, Northeastern University Press Shenyang (2002), Chinese. (2002) 
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