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On Discrete Korn's Inequality for some Nonconforming Finite Element Approaches to Linear Elasticity
Author(s) -
Attia Frank S.,
Starke Gerhard
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510383
Subject(s) - elasticity (physics) , finite element method , mathematics , inequality , linear elasticity , mathematical economics , mathematical optimization , mathematical analysis , structural engineering , engineering , materials science , composite material
Abstract The role of the discrete Korn's inequality for some nonconforming .nite element approaches to linear elasticity is discussed. Such methods enable uniform approximation in the incompressible limit and may be used in combination with a standard displacement‐based variational principle or with a least‐squares mixed formulation. A proof of the discrete Korn's inequality for a .nite element space recently proposed by Mardal, Tai and Winther is sketched. Numerical results illustrate the performance of these MTW elements for nearly incompressible linear elasticity. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)