Mixed finite elements for elasticity on quadrilateral meshes

Douglas N. Arnold, Gerard Awanou, Weifeng Qiu

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21 Scopus citations


We present stable mixed finite elements for planar linear elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three primary variables, the stress tensor, the displacement vector field, and the scalar rotation. We develop and analyze a stable family of methods, indexed by an integer r ≥ 2 and with rate of convergence in the L2 norm of order r for all the variables. The methods use Raviart–Thomas elements for the stress, piecewise tensor product polynomials for the displacement, and piecewise polynomials for the rotation. We also present a simple first order element, not belonging to this family. It uses the lowest order BDM elements for the stress, and piecewise constants for the displacement and rotation, and achieves first order convergence for all three variables.

Original languageEnglish (US)
Pages (from-to)553-572
Number of pages20
JournalAdvances in Computational Mathematics
Issue number3
StatePublished - Jun 22 2015

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.


  • Linear elasticity
  • Mixed finite element method
  • Quadrilateral elements


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