Finite elements for symmetric tensors in three dimensions

Douglas N. Arnold, Gerard Awanou, Ragnar Winther

Research output: Contribution to journalArticlepeer-review

137 Scopus citations


We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger-Reissner mixed formulation of the elasticty equations, when standard discontinuous finite element spaces are used to approximate the displacement field. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and there is one for each positive value of the polynomial degree used for the displacements. For each degree, these provide a stable finite element discretization. The construction of the spaces is closely tied to discretizations of the elasticity complex and can be viewed as the three-dimensional analogue of the triangular element family for plane elasticity previously proposed by Arnold and Winther.

Original languageEnglish (US)
Pages (from-to)1229-1251
Number of pages23
JournalMathematics of Computation
Issue number263
StatePublished - Jul 2008


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