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An alternative high‐order finite element formulation for cylindrical field problems
Author(s) -
Daly P.
Publication year - 1983
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.1620190710
Subject(s) - finite element method , interpolation (computer graphics) , convergence (economics) , mathematics , field (mathematics) , simple (philosophy) , order (exchange) , mixed finite element method , mathematical analysis , mathematical optimization , calculus (dental) , geometry , structural engineering , engineering , mechanical engineering , pure mathematics , epistemology , finance , frame (networking) , medicine , philosophy , dentistry , economics , economic growth
Earlier formulations of the finite element approach to cylindrical ( rz ) field problems led initially to variational expressions containing a simple term in 1/ r and consequent attempts to remove it by appropriate choice of interpolation functions. The present paper uses new interpolation functions which ensure that the field behaviour near the axis is correctly modelled. High‐order finite elements up to order four are derived and tested on a special cylindrical geometry to confirm, in a practical case, the theoretical claims of improved rates of convergence in solving problems of engineering significance.