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2018 Numerical studies of serendipity and tensor product elements for eigenvalue problems
Andrew Gillette, Craig Gross, Ken Plackowski
Involve 11(4): 661-678 (2018). DOI: 10.2140/involve.2018.11.661

Abstract

While the use of finite element methods for the numerical approximation of eigenvalues is a well-studied problem, the use of serendipity elements for this purpose has received little attention in the literature. We show by numerical experiments that serendipity elements, which are defined on a square reference geometry, can attain the same order of accuracy as their tensor product counterparts while using dramatically fewer degrees of freedom. In some cases, the serendipity method uses only 50% as many basis functions as the tensor product method while still producing the same numerical approximation of an eigenvalue. To encourage the further use and study of serendipity elements, we provide a table of serendipity basis functions for low-order cases and a Mathematica file that can be used to generate the basis functions for higher-order cases.

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Andrew Gillette. Craig Gross. Ken Plackowski. "Numerical studies of serendipity and tensor product elements for eigenvalue problems." Involve 11 (4) 661 - 678, 2018. https://doi.org/10.2140/involve.2018.11.661

Information

Received: 17 April 2017; Accepted: 22 July 2017; Published: 2018
First available in Project Euclid: 28 March 2018

zbMATH: 06864402
MathSciNet: MR3778918
Digital Object Identifier: 10.2140/involve.2018.11.661

Subjects:
Primary: 35P15 , 41A25 , 65H17 , 65N30

Keywords: $h$-refinement , $p$-refinement , eigenvalue approximation , serendipity finite elements

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2018
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