Vol. 11, No. 4, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Numerical studies of serendipity and tensor product elements for eigenvalue problems

Andrew Gillette, Craig Gross and Ken Plackowski

Vol. 11 (2018), No. 4, 661–678
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.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/involve

We have not been able to recognize your IP address 34.232.51.240 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Keywords
serendipity finite elements, eigenvalue approximation, $h$-refinement, $p$-refinement
Mathematical Subject Classification 2010
Primary: 35P15, 41A25, 65H17, 65N30
Milestones
Received: 17 April 2017
Accepted: 22 July 2017
Published: 15 January 2018

Communicated by Antonia Vecchio
Authors
Andrew Gillette
Department of Mathematics
University of Arizona
Tucson, AZ
United States
Craig Gross
Department of Mathematics
University of Arizona
Tucson, AZ
United States
Ken Plackowski
Department of Mathematics
University of Arizona
Tucson, AZ
United States