# 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

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topXiaofei 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 -

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