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.

翻译：我们用开放源的有限元素包Firedrake 演示了三角精度有限元素组。 新的元素可以在软件套件中无缝地用于需要1美元、\hcurl 或\hdiv-conform 元素的方块或立方体间的问题。 为了测试三角精度元素与传统高压产品元素的比较效果如何,我们进行了一系列数字实验,包括原始 Poisson、混合Poisson 和 Maxwell cavity egenvalu 问题。 总的来说,我们发现三角精度元素与预期的相同,与各自的发光产品元素相同,同时能够在解决某些问题所需的时间或记忆中节省大量时间或记忆。