Bringing trimmed serendipity methods to computational practice in Firedrake
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Published version
Author(s)
Type
Journal Article
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.
Date Issued
2022-03
Date Acceptance
2021-10-01
Citation
ACM Transactions on Mathematical Software, 2022, 48 (1)
ISSN
0098-3500
Publisher
Association for Computing Machinery (ACM)
Journal / Book Title
ACM Transactions on Mathematical Software
Volume
48
Issue
1
Copyright Statement
© 2022 Copyright held by the owner/author(s). This work is licensed under a Creative Commons Attribution International 4.0 License.
License URL
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000759468700009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Subjects
Computer Science
Computer Science, Software Engineering
EXTERIOR CALCULUS
FEM
finite element method
firedrake
H(DIV)
Mathematics
Mathematics, Applied
MIXED FINITE-ELEMENTS
PDEs
Physical Sciences
Science & Technology
Technology
trimmed serendipity
Publication Status
Published
Article Number
8
Date Publish Online
2022-02-16