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A Second Elasticity Element Using the Matrix Bubble
IMA Journal of Numerical Analysis
  • Jay Gopalakrishnan, Portland State University
  • Johnny Guzmán, Brown University
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Publication Date
  • Finite element method,
  • Boundary value problems,
  • Elasticity

We presented a family of finite elements that use a polynomial space augmented by certain matrix bubbles in Cockburn et al. (2010) A new elasticity element made for enforcing weak stress symmetry. Math. Comput., 79, 1331–1349 . In this sequel we exhibit a second family of elements that use the same matrix bubble. This second element uses a stress space smaller than the first while maintaining the same space for rotations (which are the Lagrange multipliers corresponding to a weak symmetry constraint). The space of displacements is of one degree less than the first method. The analysis, while similar to the first, requires a few adjustments as the new Fortin projector may not preserve weak symmetry, but we are able to prove optimal convergence for all the variables. Finally, we present a sufficient condition wherein a mixed method with weakly imposed stress symmetry in fact yields an exactly symmetric stress tensor approximation.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The definitive publisher-authenticated version IMA Journal of Numerical Analysis, January 2012, Vol. 32, Issue 1 is available online at:

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Jay Gopalakrishnan and Johnny Guzmán. "A Second Elasticity Element Using the Matrix Bubble" IMA Journal of Numerical Analysis (2011)
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