Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients

Xiaofei Guan; Mingxia Li; Wenming He; Zhengwu Jiang

Open Mathematics (2014)

  • Volume: 12, Issue: 11, page 1733-1747
  • ISSN: 2391-5455

Abstract

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In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x 0 for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(h p+1 |ln h|2) and O(h p+2 |ln h|2) when p (≥ 3) is odd and p (≥ 4) is even, respectively. Meanwhile, the results show that the combination of the weak estimates and local symmetric technique is also effective for superconvergence analysis of the second order elliptic equation with variable coefficients.

How to cite

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Xiaofei Guan, et al. "Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients." Open Mathematics 12.11 (2014): 1733-1747. <http://eudml.org/doc/269225>.

@article{XiaofeiGuan2014,
abstract = {In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x 0 for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(h p+1 |ln h|2) and O(h p+2 |ln h|2) when p (≥ 3) is odd and p (≥ 4) is even, respectively. Meanwhile, the results show that the combination of the weak estimates and local symmetric technique is also effective for superconvergence analysis of the second order elliptic equation with variable coefficients.},
author = {Xiaofei Guan, Mingxia Li, Wenming He, Zhengwu Jiang},
journal = {Open Mathematics},
keywords = {Second order elliptic problem; High-degree triangular element; Superconvergence; Local symmetric technique; Weak estimates; second-order elliptic problem; high-degree triangular elements; superconvergence; local symmetric technique; weak estimates},
language = {eng},
number = {11},
pages = {1733-1747},
title = {Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients},
url = {http://eudml.org/doc/269225},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Xiaofei Guan
AU - Mingxia Li
AU - Wenming He
AU - Zhengwu Jiang
TI - Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients
JO - Open Mathematics
PY - 2014
VL - 12
IS - 11
SP - 1733
EP - 1747
AB - In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x 0 for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(h p+1 |ln h|2) and O(h p+2 |ln h|2) when p (≥ 3) is odd and p (≥ 4) is even, respectively. Meanwhile, the results show that the combination of the weak estimates and local symmetric technique is also effective for superconvergence analysis of the second order elliptic equation with variable coefficients.
LA - eng
KW - Second order elliptic problem; High-degree triangular element; Superconvergence; Local symmetric technique; Weak estimates; second-order elliptic problem; high-degree triangular elements; superconvergence; local symmetric technique; weak estimates
UR - http://eudml.org/doc/269225
ER -

References

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