Physical Sciences and Mathematics Commons^™

A New Elasticity Element Made For Enforcing Weak Stress Symmetry, Bernardo Cockburn, Jay Gopalakrishnan, Johnny Guzmán

Mathematics and Statistics Faculty Publications and Presentations

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 + …