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Numerische Mathematik

, Volume 53, Issue 1–2, pp 123–141 | Cite as

A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element formulation

  • Leopoldo P. Franca
  • Thomas J. R. Hughes
  • Abimael F. D. Loula
  • Isidoro Miranda
Article

Summary

Adding to the classical Hellinger Reissner formulation another residual form of the equilibrium equation, a new Petrov-Galerkin finite element method is derived. It fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations, including equal-order discontinuous stress and continuous displacement interpolations which are unstable within the Galerkin approach. Error estimates are presented using the Babuška-Brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method.

Subject Classifications

AMS(MOS):65N30 CR: G1.8 

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Leopoldo P. Franca
    • 1
  • Thomas J. R. Hughes
    • 1
  • Abimael F. D. Loula
    • 2
  • Isidoro Miranda
    • 3
  1. 1.Division of Applied MechanicsStanford UniversityStanfordUSA
  2. 2.Laboratório Nacional de Computação Cientifica-LNCC/CNPqRio de JaneiroBrazil
  3. 3.Escuela Superior de Ingenieros IndustrialesSan SebastiánSpain

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