Locally pointwise superconvergence of the tensor-product finite element in three dimensions

Jinghong Liu; Liu, Wen; Qiding Zhu

Applications of Mathematics (2019)

  • Volume: 64, Issue: 4, page 383-396
  • ISSN: 0862-7940

Abstract

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Consider a second-order elliptic boundary value problem in three dimensions with locally smooth coefficients and solution. Discuss local superconvergence estimates for the tensor-product finite element approximation on a regular family of rectangular meshes. It will be shown that, by the estimates for the discrete Green’s function and discrete derivative Green’s function, and the relationship of norms in the finite element space such as L 2 -norms, W 1 , ∞ -norms, and negative-norms in locally smooth subsets of the domain Ω , locally pointwise superconvergence occurs in function values and derivatives.

How to cite

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Liu, Jinghong, Liu, Wen, and Zhu, Qiding. "Locally pointwise superconvergence of the tensor-product finite element in three dimensions." Applications of Mathematics 64.4 (2019): 383-396. <http://eudml.org/doc/294603>.

@article{Liu2019,
abstract = {Consider a second-order elliptic boundary value problem in three dimensions with locally smooth coefficients and solution. Discuss local superconvergence estimates for the tensor-product finite element approximation on a regular family of rectangular meshes. It will be shown that, by the estimates for the discrete Green’s function and discrete derivative Green’s function, and the relationship of norms in the finite element space such as $L^2$-norms, $W^\{1,\infty \}$-norms, and negative-norms in locally smooth subsets of the domain $\Omega $, locally pointwise superconvergence occurs in function values and derivatives.},
author = {Liu, Jinghong, Liu, Wen, Zhu, Qiding},
journal = {Applications of Mathematics},
keywords = {tensor-product finite element; local superconvergence; discrete Green's function},
language = {eng},
number = {4},
pages = {383-396},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Locally pointwise superconvergence of the tensor-product finite element in three dimensions},
url = {http://eudml.org/doc/294603},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Liu, Jinghong
AU - Liu, Wen
AU - Zhu, Qiding
TI - Locally pointwise superconvergence of the tensor-product finite element in three dimensions
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 383
EP - 396
AB - Consider a second-order elliptic boundary value problem in three dimensions with locally smooth coefficients and solution. Discuss local superconvergence estimates for the tensor-product finite element approximation on a regular family of rectangular meshes. It will be shown that, by the estimates for the discrete Green’s function and discrete derivative Green’s function, and the relationship of norms in the finite element space such as $L^2$-norms, $W^{1,\infty }$-norms, and negative-norms in locally smooth subsets of the domain $\Omega $, locally pointwise superconvergence occurs in function values and derivatives.
LA - eng
KW - tensor-product finite element; local superconvergence; discrete Green's function
UR - http://eudml.org/doc/294603
ER -

References

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