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Volume 23, Issue 3
An Anisotropic Nonconforming Finite Element with Some Superconvergence Results

Dong-Yang Shi, Shi-Peng Mao & Shao-Chun Chen

J. Comp. Math., 23 (2005), pp. 261-274.

Published online: 2005-06

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  • Abstract

The main aim of this paper is to study the error estimates of a nonconforming finite element with some superconvergence results under anisotropic meshes. The anisotropic interpolation error and consistency error estimates are obtained by using some novel approaches and techniques, respectively. Furthermore, the superclose and a superconvergence estimate on the central points of elements are also obtained without the regularity assumption and quasi-uniform assumption requirement on the meshes. Finally, a numerical test is carried out, which coincides with our theoretical analysis.

  • Keywords

Anisotropic meshes, Nonconforming finite element, Interpolation error and consistency error estimates, Superclose, Superconvergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-261, author = {Dong-Yang Shi, Shi-Peng Mao and Shao-Chun Chen}, title = {An Anisotropic Nonconforming Finite Element with Some Superconvergence Results}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {3}, pages = {261--274}, abstract = {

The main aim of this paper is to study the error estimates of a nonconforming finite element with some superconvergence results under anisotropic meshes. The anisotropic interpolation error and consistency error estimates are obtained by using some novel approaches and techniques, respectively. Furthermore, the superclose and a superconvergence estimate on the central points of elements are also obtained without the regularity assumption and quasi-uniform assumption requirement on the meshes. Finally, a numerical test is carried out, which coincides with our theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8814.html} }
TY - JOUR T1 - An Anisotropic Nonconforming Finite Element with Some Superconvergence Results AU - Dong-Yang Shi, Shi-Peng Mao & Shao-Chun Chen JO - Journal of Computational Mathematics VL - 3 SP - 261 EP - 274 PY - 2005 DA - 2005/06 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8814.html KW - Anisotropic meshes, Nonconforming finite element, Interpolation error and consistency error estimates, Superclose, Superconvergence. AB -

The main aim of this paper is to study the error estimates of a nonconforming finite element with some superconvergence results under anisotropic meshes. The anisotropic interpolation error and consistency error estimates are obtained by using some novel approaches and techniques, respectively. Furthermore, the superclose and a superconvergence estimate on the central points of elements are also obtained without the regularity assumption and quasi-uniform assumption requirement on the meshes. Finally, a numerical test is carried out, which coincides with our theoretical analysis.

Dong-Yang Shi, Shi-Peng Mao and Shao-Chun Chen. (2005). An Anisotropic Nonconforming Finite Element with Some Superconvergence Results. Journal of Computational Mathematics. 23 (3). 261-274. doi:
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