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Dual analysis for heat conduction problems by finite elements
Author(s) -
De Veubeke B. M. Fraeijs,
Hugge M. A.
Publication year - 1972
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.1620050107
Subject(s) - finite element method , dual (grammatical number) , convergence (economics) , thermal conduction , minification , connection (principal bundle) , mathematics , mixed finite element method , function (biology) , mathematical analysis , mathematical optimization , geometry , physics , thermodynamics , art , literature , economics , economic growth , evolutionary biology , biology
An alternative approach to the usual finite element treatment of steady‐state temperature problems is presented, using approximations for the field of the dual variables. The appropriate extremum principle is established and its minimization is discussed in connection with a plane triangular finite element process. Original heat flow elements are derived: in conjunction with temperature elements, they enable dual analysis of a given structure and an important estimate of the convergence to the true solution by upper and lower bounds to the dissipation function, as illustrated by means of several examples.