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An additional stiffness parameter measure of error of the second kind in the finite element method
Author(s) -
Prathap Gangan
Publication year - 1985
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.1620210603
Subject(s) - spurious relationship , finite element method , logarithm , mathematics , interpolation (computer graphics) , measure (data warehouse) , limiting , field (mathematics) , norm (philosophy) , stiffness , computer science , mathematical analysis , statistics , structural engineering , engineering , animation , mechanical engineering , computer graphics (images) , database , law , political science , pure mathematics
Conventional error analyses norms in the finite element method are based on the percentage error or its equivalent in some computed value as compared to the theoretically predicted value. In problems where two or more field variables are coupled, it is possible that if the field interpolation functions do not ‘consistently’ reproduce limiting situations of physical behaviour, there may be very large errors which are exaggerated enormously when some structural parameters become indefinitely large in a penalty limiting sense. The percentage error norms therefore saturate quickly to a value approaching 100 per cent and do not sensibly reflect the relationship between error and the structural parameter, even on a logarithmic plot. Errors due to these spurious constraints have recently been recognized as belonging to a special class described as ‘errors of the second kind’. A new error norm, called the additional stiffening parameter, helps to recognize the manner in which errors of the second kind can be blown out, of propprtion by a large variation in some structural parameter. Recent investigations in some multi‐field problems are summarized here to demonstrate the usefulness of this concept.