Premium
The patch test for mixed formulations
Author(s) -
Zienkiewicz O. C.,
Qu S.,
Taylor R. L.,
Nakazawa S.
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.1620231007
Subject(s) - mathematics , limiting , simple (philosophy) , convergence (economics) , compressibility , elasticity (physics) , displacement (psychology) , mathematical optimization , mechanics , engineering , materials science , physics , mechanical engineering , psychology , philosophy , epistemology , economics , composite material , psychotherapist , economic growth
This paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence. The general algebraic conditions of Babuska and Brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems. The test is also applied to mixed displacement—strain formulations of elasticity, and limiting formulations are noted.