Optimal second order rectangular elasticity elements with weakly symmetric stress

Mika Juntunen, Jeong Lee

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)


We present new second order rectangular mixed finite elements for linear elasticity where the symmetry condition on the stress is imposed weakly with a Lagrange multiplier. The key idea in constructing the new finite elements is enhancing the stress space of the Awanou's rectangular elements (rectangular Arnold-Falk-Winther elements) using bubble functions. The proposed elements have only 18 and 63 degrees of freedom for the stress in two and three dimensions, respectively, and they achieve the optimal second order convergence of errors for all the unknowns. We also present a new simple a priori error analysis and provide numerical results illustrating our analysis.

Original languageEnglish
Pages (from-to)425-445
Number of pages21
JournalBIT Numerical Mathematics
Issue number2
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed


  • Elasticity
  • Mixed finite element
  • Rectangular finite element
  • Weakly imposed symmetry

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