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Volume 23, Issue 6
Constrained Quadrilateral Nonconforming Rotated $Q_1$ Element

Jun Hu & Zhong-Ci Shi

J. Comp. Math., 23 (2005), pp. 561-586.

Published online: 2005-12

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  • Abstract

In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated $Q$1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green's function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.

  • Keywords

Constrained, Nonconforming Rotated $Q_1$ element, Superconvergence, Postprocess.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-23-561, author = {Jun Hu and Zhong-Ci Shi}, title = {Constrained Quadrilateral Nonconforming Rotated $Q_1$ Element}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {6}, pages = {561--586}, abstract = {

In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated $Q$1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green's function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8839.html} }
TY - JOUR T1 - Constrained Quadrilateral Nonconforming Rotated $Q_1$ Element AU - Jun Hu & Zhong-Ci Shi JO - Journal of Computational Mathematics VL - 6 SP - 561 EP - 586 PY - 2005 DA - 2005/12 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8839.html KW - Constrained, Nonconforming Rotated $Q_1$ element, Superconvergence, Postprocess. AB -

In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated $Q$1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green's function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.

Jun Hu and Zhong-Ci Shi. (2005). Constrained Quadrilateral Nonconforming Rotated $Q_1$ Element. Journal of Computational Mathematics. 23 (6). 561-586. doi:
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