  We present an implementation of the trimmed serendipity finite element
family, using the open source finite element package Firedrake. The new
elements can be used seamlessly within the software suite for problems
requiring $H^1$, \hcurl, or \hdiv-conforming elements on meshes of squares or
cubes. To test how well trimmed serendipity elements perform in comparison to
traditional tensor product elements, we perform a sequence of numerical
experiments including the primal Poisson, mixed Poisson, and Maxwell cavity
eigenvalue problems. Overall, we find that the trimmed serendipity elements
converge, as expected, at the same rate as the respective tensor product
elements while being able to offer significant savings in the time or memory
required to solve certain problems.
