The patch test—a condition for assessing FEM convergence | Zendy

Taylor R. L. | Zendy; Simo J. C. | Zendy; Zienkiewicz O. C. | Zendy; Chan A. C. H. | Zendy

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The patch test—a condition for assessing FEM convergence

Author(s) -

Taylor R. L.,

Simo J. C.,

Zienkiewicz O. C.,

Chan A. C. H.

Publication year - 1986

Publication title -

international journal for numerical methods in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.421

H-Index - 168

eISSN - 1097-0207

pISSN - 0029-5981

DOI - 10.1002/nme.1620220105

Subject(s) - convergence (economics) , finite element method , consistency (knowledge bases) , test (biology) , stability (learning theory) , mathematics , computer science , engineering , structural engineering , geometry , geology , paleontology , machine learning , economic growth , economics

This paper discusses various forms of the Irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency, Further, it is shown that the test can be applied for verification of stability requirements, thus providing also a sufficient condition of convergence. The patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms.

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