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Superconvergent derivatives: A Taylor series analysis
Author(s) -
Mackin R. J.,
Carey G. F.
Publication year - 1989
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.1620280302
Subject(s) - superconvergence , taylor series , constructive , convergence (economics) , series (stratigraphy) , mathematics , finite element method , class (philosophy) , series expansion , constructive proof , calculus (dental) , mathematical analysis , computer science , discrete mathematics , engineering , geology , structural engineering , economics , medicine , paleontology , process (computing) , dentistry , artificial intelligence , economic growth , operating system
An analysis, based on the use of Taylor series expansions, is developed to determine accuracy estimates for derivatives in one and two dimensions computed by differentiation of a finite‐element interpolant or approximation. The analysis clarifies some issues concerning special points at which the derivatives are believed to be exceptionally accurate with higher convergence rates (superconvergence). Moreover, it leads directly to a class of post‐processing strategies for the derivatives and offers a more direct constructive approach to the subject.