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Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities
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@Article{JCM-28-11,
author = {},
title = {Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities},
journal = {Journal of Computational Mathematics},
year = {2010},
volume = {28},
number = {1},
pages = {11--31},
abstract = { For the linear finite element solution to the Poisson equation, we show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^(2)-projection from the piecewise constant field to the continuous and piecewise linear finite element space gives a better approximation in the H^(1)-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution. },
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2009.09-m1002},
url = {http://global-sci.org/intro/article_detail/jcm/8504.html}
}
TY - JOUR
T1 - Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities
JO - Journal of Computational Mathematics
VL - 1
SP - 11
EP - 31
PY - 2010
DA - 2010/02
SN - 28
DO - http://doi.org/10.4208/jcm.2009.09-m1002
UR - https://global-sci.org/intro/article_detail/jcm/8504.html
KW - Superconvergence
KW - Graded meshes
KW - Weighted Sobolev spaces
KW - Singular solutions
KW - The finite element method
KW - Gradient recovery schemes
AB - For the linear finite element solution to the Poisson equation, we show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^(2)-projection from the piecewise constant field to the continuous and piecewise linear finite element space gives a better approximation in the H^(1)-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.
Long Chen & Hengguang Li. (2019). Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities.
Journal of Computational Mathematics. 28 (1).
11-31.
doi:10.4208/jcm.2009.09-m1002
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