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@article{Crum:2022:10.1145/3490485,
author = {Crum, J and Cheng, C and Ham, DA and Mitchell, L and Kirby, RC and Levine, JA and Gillette, A},
doi = {10.1145/3490485},
journal = {ACM Transactions on Mathematical Software},
title = {Bringing trimmed serendipity methods to computational practice in Firedrake},
url = {http://dx.doi.org/10.1145/3490485},
volume = {48},
year = {2022}
}

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TY  - JOUR
AB  - 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.
AU  - Crum,J
AU  - Cheng,C
AU  - Ham,DA
AU  - Mitchell,L
AU  - Kirby,RC
AU  - Levine,JA
AU  - Gillette,A
DO  - 10.1145/3490485
PY  - 2022///
SN  - 0098-3500
TI  - Bringing trimmed serendipity methods to computational practice in Firedrake
T2  - ACM Transactions on Mathematical Software
UR  - http://dx.doi.org/10.1145/3490485
UR  - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000759468700009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
UR  - https://dl.acm.org/doi/10.1145/3490485
UR  - http://hdl.handle.net/10044/1/109480
VL  - 48
ER  -

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