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Volumetric locking in natural neighbour Galerkin methods
Author(s) -
González D.,
Cueto E.,
Doblaré M.
Publication year - 2004
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.1085
Subject(s) - interpolation (computer graphics) , limit (mathematics) , mathematics , partition (number theory) , galerkin method , finite element method , compressibility , polynomial , calculus (dental) , mathematical analysis , computer science , structural engineering , combinatorics , engineering , mechanics , physics , artificial intelligence , motion (physics) , medicine , dentistry
The behaviour of natural neighbour Galerkin mixed approximation is described at the incompressible limit. Traditional natural elements based on the Sibson mixed interpolation do not verify the LBB (or inf–sup) condition. Here, a study of the possible benefits of enriching the interpolation is considered using the partition of unity paradigm. Different enrichments were tested leading to different reproducing properties. Results concerning the numerical verification of the inf–sup tests are addressed. Also the convenience of using different approximations developed in this work is analysed. Enrichment with the polynomial field {1, xy } seems to verify the LBB condition. Its behaviour has proven to be very similar to the MINI Finite Element, widely used in the literature. Examples proving these results are provided. Copyright © 2004 John Wiley & Sons, Ltd.