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A NEW ELASTICITY ELEMENT MADE FOR ENFORCING WEAK STRESS SYMMETRY

BERNARDO COCKBURN, JAYADEEP GOPALAKRISHNAN and JOHNNY GUZMÁN
Mathematics of Computation
Vol. 79, No. 271 (JULY 2010), pp. 1331-1349
Stable URL: http://www.jstor.org/stable/20779103
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A NEW ELASTICITY ELEMENT MADE FOR ENFORCING WEAK STRESS SYMMETRY
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Abstract

We introduce a new mixed method for linear elasticity. The novelty is a simplicial element for the approximate stress. For every positive integer k, the row-wise divergence of the element space spans the set of polynomials of total degree k. The degrees of freedom are suited to achieve continuity of the normal stresses. What makes the element distinctive is that its dimension is the smallest required for enforcing a weak symmetry condition on the approximate stress. This is achieved using certain "bubble matrices", which are special divergence-free matrix-valued polynomials. We prove that the approximation error is of order k + 1 in both the displacement and the stress, and that a postprocessed displacement approximation converging at order k + 2 can be computed element by element. We also show that the globally coupled degrees of freedom can be reduced by hybridization to those of a displacement approximation on the element boundaries.

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