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A hybrid element formulation for the three‐dimensional penalty finite element analysis of incompressible fluids
Author(s) -
Jog C. S.
Publication year - 2007
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.2062
Subject(s) - finite element method , mixed finite element method , penalty method , extended finite element method , finite element limit analysis , mathematics , compressibility , newtonian fluid , stress (linguistics) , degrees of freedom (physics and chemistry) , smoothed finite element method , smoothing , mathematical analysis , mathematical optimization , classical mechanics , physics , mechanics , boundary knot method , engineering , structural engineering , linguistics , philosophy , statistics , quantum mechanics , boundary element method
Abstract This work presents a hybrid element formulation for the three‐dimensional penalty finite element analysis of incompressible Newtonian fluids. The formulation is based on a mixed variational statement in which velocity and stresses are treated as independent field variables. The main advantage of this formulation is that it bypasses the use of ad hoc techniques such as selective reduced integration that are commonly used in penalty‐based finite element formulations, and directly yields high accuracy for the velocity and stress fields without the need to carry out smoothing. In addition, since the stress degrees of freedom are condensed out at an element level, the cost of solving for the global degrees of freedom is the same as in a standard penalty finite element method, although the gain in accuracy for both the velocity and stress (including the pressure) fields is quite significant. Copyright © 2007 John Wiley & Sons, Ltd.