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Volume 29, Issue 2
A Note on the Nonconforming Finite Elements for Elliptic Problems

Boran Gao, Shuo Zhang & Ming Wang

DOI: 10.4208/jcm.1009-m3246

J. Comp. Math., 29 (2011), pp. 215-226.

Published online: 2011-04

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  • Abstract

In this paper, a class of rectangular finite elements for $2m$-th-oder elliptic boundary value problems in $n$-dimension ($m,n\geq1$) is proposed in a canonical fashion, which includes the ($2m-1$)-th Hermite interpolation element ($n=1$), the $n$-linear finite element ($m=1$) and the Adini element ($m=2$). A nonconforming triangular finite element for the plate bending problem, with convergent order $\mathcal{O}(h^2)$, is also proposed.

  • Keywords

Nonconforming finite element, Elliptic boundary value problem, Plate bending problem.

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-29-215, author = {Boran Gao, Shuo Zhang and Ming Wang}, title = {A Note on the Nonconforming Finite Elements for Elliptic Problems}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {2}, pages = {215--226}, abstract = {

In this paper, a class of rectangular finite elements for $2m$-th-oder elliptic boundary value problems in $n$-dimension ($m,n\geq1$) is proposed in a canonical fashion, which includes the ($2m-1$)-th Hermite interpolation element ($n=1$), the $n$-linear finite element ($m=1$) and the Adini element ($m=2$). A nonconforming triangular finite element for the plate bending problem, with convergent order $\mathcal{O}(h^2)$, is also proposed.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1009-m3246}, url = {http://global-sci.org/intro/article_detail/jcm/8474.html} }
TY - JOUR T1 - A Note on the Nonconforming Finite Elements for Elliptic Problems AU - Boran Gao, Shuo Zhang & Ming Wang JO - Journal of Computational Mathematics VL - 2 SP - 215 EP - 226 PY - 2011 DA - 2011/04 SN - 29 DO - http://doi.org/10.4208/jcm.1009-m3246 UR - https://global-sci.org/intro/article_detail/jcm/8474.html KW - Nonconforming finite element, Elliptic boundary value problem, Plate bending problem. AB -

In this paper, a class of rectangular finite elements for $2m$-th-oder elliptic boundary value problems in $n$-dimension ($m,n\geq1$) is proposed in a canonical fashion, which includes the ($2m-1$)-th Hermite interpolation element ($n=1$), the $n$-linear finite element ($m=1$) and the Adini element ($m=2$). A nonconforming triangular finite element for the plate bending problem, with convergent order $\mathcal{O}(h^2)$, is also proposed.

Boran Gao, Shuo Zhang and Ming Wang. (2011). A Note on the Nonconforming Finite Elements for Elliptic Problems. Journal of Computational Mathematics. 29 (2). 215-226. doi:10.4208/jcm.1009-m3246
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