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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.