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

Zhong-Ci Shi

DOI:

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} }
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