@article{a61537542f4c431b92d46e1b0dbe1937,
title = "Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake",
abstract = "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. ",
keywords = "FEM, PDEs, finite element method, firedrake, trimmed serendipity",
author = "Justin Crum and Cyrus Cheng and Ham, {David A.} and Lawrence Mitchell and Kirby, {Robert C.} and Levine, {Joshua A.} and Andrew Gillette",
note = "Funding Information: This work was supported by National Science Foundation (NSF) Collaborative Research Awards No. DMS-1913094 and No. DMS-1912653 and by U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under Award No. DE-SC-0019039. Authors{\textquoteright} addresses: J. Crum and A. Gillette, University of Arizona, Department of Mathematics, Tucson, AZ, USA; emails: {jcrum, agillette}@math.arizona.edu; C. Cheng and D. A. Ham, Imperial College London, Department of Mathematics, London, SW7 2AZ, UK; emails: cyrus.cheng15@alumni.imperial.ac.uk, david.ham@imperial.ac.uk; L. Mitchell, Durham University, Department of Computer Science, Upper Mountjoy, Durham, DH1 3LE, UK; email: lawrence.mitchell@durham. ac.uk; R. C. Kirby, Baylor University, Department of Mathematics, 1410 S. 4th Street, Waco, TX, USA; email: robert_kirby@ baylor.edu; J. A. Levine, University of Arizona, Department of Computer Science, Tucson, AZ, USA; email: josh@email. arizona.edu. Publisher Copyright: {\textcopyright} 2022 Copyright held by the owner/author(s).",
year = "2022",
month = mar,
doi = "10.1145/3490485",
language = "English (US)",
volume = "48",
journal = "ACM Transactions on Mathematical Software",
issn = "0098-3500",
publisher = "Association for Computing Machinery (ACM)",
number = "1",
}