  The Arnold-Winther element successfully discretizes the Hellinger-Reissner
variational formulation of linear elasticity; its development was one of the
key early breakthroughs of the finite element exterior calculus. Despite its
great utility, it is not available in standard finite element software, because
its degrees of freedom are not preserved under the standard Piola push-forward.
In this work we apply the novel transformation theory recently developed by
Kirby [SMAI-JCM, 4:197-224, 2018] to devise the correct map for transforming
the basis on a reference cell to a generic physical triangle. This enables the
use of the Arnold-Winther elements, both conforming and nonconforming, in the
widely-used Firedrake finite element software, composing with its advanced
symbolic code generation and geometric multigrid functionality. Similar results
also enable the correct transformation of the Mardal-Tai-Winther element for
incompressible fluid flow. We present numerical results for both elements,
verifying the correctness of our theory.
