Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake

Justin Crum, Cyrus Cheng, David A. Ham, Lawrence Mitchell, Robert C. Kirby, Joshua A. Levine, Andrew Gillette

Research output: Contribution to journalArticlepeer-review


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 H1, H(curl), or H(div)-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.

Original languageEnglish (US)
Article number8
JournalACM Transactions on Mathematical Software
Issue number1
StatePublished - Mar 2022
Externally publishedYes


  • FEM
  • PDEs
  • finite element method
  • firedrake
  • trimmed serendipity

ASJC Scopus subject areas

  • Software
  • Applied Mathematics


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