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A finite element method for nearly incompressible elasticity problems


Authors: Dietrich Braess and Pingbing Ming
Journal: Math. Comp. 74 (2005), 25-52
MSC (2000): Primary 65N30, 74S05, 74B20
DOI: https://doi.org/10.1090/S0025-5718-04-01662-X
Published electronically: April 28, 2004
MathSciNet review: 2085401
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Abstract: A finite element method is considered for dealing with nearly incompressible material. In the case of large deformations the nonlinear character of the volumetric contribution has to be taken into account. The proposed mixed method avoids volumetric locking also in this case and is robust for $\lambda \to \infty$ (with $\lambda$ being the well-known Lamé constant). Error estimates for the $L^{\infty}$-norm are crucial in the control of the nonlinear terms.


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Additional Information

Dietrich Braess
Affiliation: Faculty of Mathematics, Ruhr-University, 44780 Bochum, Germany
Email: braess@num.ruhr-uni-bochum.de

Pingbing Ming
Affiliation: Institute of Computational Mathematics, Chinese Academy of Sciences, POB 2719, Beijing 100080, Peoples Republic of China
Email: mpb@lsec.cc.ac.cn

DOI: https://doi.org/10.1090/S0025-5718-04-01662-X
Keywords: Incompressible elasticity, Green's functions, $L^{\infty}$-estimates.
Received by editor(s): November 7, 2001
Received by editor(s) in revised form: July 11, 2003
Published electronically: April 28, 2004
Article copyright: © Copyright 2004 American Mathematical Society