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Volume 2, Issue 3
The Generalized Patch Test for Zienkiewicz's Triangles

Zhong-Ci Shi

J. Comp. Math., 2 (1984), pp. 279-286.

Published online: 1984-02

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  • Abstract

It is proved that Zienkiewicz's triangles for plate bending problems pass Stummel's generalized patch test — a necessary and sufficient condition for convergence of nonconforming finite elements — for mesh (a) generated by three sets of parallel lines, but do not pass it when "union jack" mesh (b) or when another mesh (c) is used. In the latter two cases the approximations are divergent.

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@Article{JCM-2-279, author = {Zhong-Ci Shi}, title = {The Generalized Patch Test for Zienkiewicz's Triangles}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {3}, pages = {279--286}, abstract = {

It is proved that Zienkiewicz's triangles for plate bending problems pass Stummel's generalized patch test — a necessary and sufficient condition for convergence of nonconforming finite elements — for mesh (a) generated by three sets of parallel lines, but do not pass it when "union jack" mesh (b) or when another mesh (c) is used. In the latter two cases the approximations are divergent.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9663.html} }
TY - JOUR T1 - The Generalized Patch Test for Zienkiewicz's Triangles AU - Zhong-Ci Shi JO - Journal of Computational Mathematics VL - 3 SP - 279 EP - 286 PY - 1984 DA - 1984/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9663.html KW - AB -

It is proved that Zienkiewicz's triangles for plate bending problems pass Stummel's generalized patch test — a necessary and sufficient condition for convergence of nonconforming finite elements — for mesh (a) generated by three sets of parallel lines, but do not pass it when "union jack" mesh (b) or when another mesh (c) is used. In the latter two cases the approximations are divergent.

Zhong-Ci Shi. (1984). The Generalized Patch Test for Zienkiewicz's Triangles. Journal of Computational Mathematics. 2 (3). 279-286. doi:
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