Identifier: 2009-29
Author(s): J. Gopalakrishnan and J. Guzman
Title: A second elasticity element using the matrix bubble with tightened stress symmetry
Page count: 19 pp.
Date: 2009-09-17
Abstract:
We presented a family of finite elements that use a polynomial space aug- mented by certain matrix bubbles in [15]. 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 mul- tipliers corresponding to a weak symmetry constraint). Consequently, it generates stresses satisfying tighter weak symmetry constraints than the first method. The space of displace- ments are of one degree less than the first method. The analysis, while similar to the first, requires a few new adjustments as the new Fortin projector may not preserve weak symme- try, 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.
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