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Stabilized hybrid finite element methods based on the combination of saddle point principles of elasticity problems

Author: Tianxiao Zhou
Journal: Math. Comp. 72 (2003), 1655-1673
MSC (2000): Primary 65N12, 65N30
Published electronically: April 28, 2003
MathSciNet review: 1986798
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Abstract: How, in a discretized model, to utilize the duality and complementarity of two saddle point variational principles is considered in the paper. A homology family of optimality conditions, different from the conventional saddle point conditions of the domain-decomposed Hellinger-Reissner principle, is derived to enhance stability of hybrid finite element schemes. Based on this, a stabilized hybrid method is presented by associating element-interior displacement with an element-boundary one in a nonconforming manner. In addition, energy compatibility of strain-enriched displacements with respect to stress terms is introduced to circumvent Poisson-locking.

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Additional Information

Tianxiao Zhou
Affiliation: Aeronautical Computing Technology Research Institute, Xi’an 710068, Peoples Republic of China

Received by editor(s): October 13, 1999
Received by editor(s) in revised form: March 7, 2001
Published electronically: April 28, 2003
Additional Notes: This work was subsidized by the Special Funds for Major State Basic Research Projects (G1999032801) and the Funds for Aeronautics (00B31005)
Article copyright: © Copyright 2003 American Mathematical Society

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