The Spectral Element Method for the Steklov Eigenvalue Problem

Yan Jun Li; Yi Du Yang; Hai Bi

doi:10.4028/www.scientific.net/AMR.853.631

Paper Titles

Effect of Blank Shape and Size on the Forming Quality of Thread Shaft Rolling in Cross Wedge Rolling
p.605

Design and Realization of Robot Workplaces with Virtual and Augmented Reality Application
p.613

Algorithms for Dynamic Hardness Measurements by Scratch Testing in the Submicron and Nanometer Scale
p.619

Design of Automatic Scraping System
p.625

The Spectral Element Method for the Steklov Eigenvalue Problem
p.631

Linear Matrix Inequality and its Application in Control Theory
p.636

Study of Fault Arc Protection Based on UV Pulse Method in High Voltage Switchgear
p.641

Intelligent Aquaculture Monitoring System Based on Fieldbus
p.646

A Survey on Randomized Sampling-Based Path Optimization Methods
p.652

HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 853The Spectral Element Method for the Steklov...

The Spectral Element Method for the Steklov Eigenvalue Problem

Abstract:

This paper discusses the spectral element approximation with LGL node basis for the Steklov eigenvalue problem, and analyzes the a priori error estimates. Finally, numerical experi-ments on the square and the L-shaped domain are carried out to get very accurate approximations by the spectral element method.

You might also be interested in these eBooks

Materials Science, Machinery and Energy Engineering

View Preview

Info:

Periodical:

Advanced Materials Research (Volume 853)

Pages:

631-635

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.853.631

Citation:

Cite this paper

Online since:

December 2013

Authors:

Yan Jun Li, Yi Du Yang, Hai Bi*

Keywords:

Coupled Fluid-Solid Vibrations, Error Estimates, Spectral Element Method, Steklov Eigenvalue Problem

Export:

RIS, BibTeX

Price:

Permissions:

Request Permissions

* - Corresponding Author

References

[1] S. Bergman and M. Schiffer, Kernel Functions and Elliptic Differential Equations in Mathema-tical Physics, Academic Press, New York, USA (1953).

Google Scholar

[2] A. Alonso and A. Dello Russo, Spectral approximation of variationally posed eigenvalue prob-lems by non-conforming methods, J. Comput. Appl. Math., Vol. 223(2009), pp.177-197.

DOI: 10.1016/j.cam.2008.01.008

Google Scholar

[3] A. Bermudez, R. Rodriguez and D. Santamarina, A finite element solution of an added mass formulation for coupled fluid-soild vibrations, Numer. Math., Vol. 87(2000), pp.201-227.

DOI: 10.1007/s002110000175

Google Scholar

[4] A. B. Andreew and T. D. Todorov, Isoparametric finite element approximation of a Steklov eigenvalue problem, IMA J. Numer. Anal., (2004), pp.309-322.

DOI: 10.1093/imanum/24.2.309

Google Scholar

[5] Y. D. Yang, Q. Li and S. R. Li, Nonconforming finite element approximations of the Steklov eigenvalue problem, Appl. Numer. Math., Vol. 59(2009), pp.2388-2401.

DOI: 10.1016/j.apnum.2009.04.005

Google Scholar

[6] E. M. Garau and P. Morin, Convergence and quasi-optimality of adaptive FEM for Steklov eigenvalue problems, IMA J. Anal., Vol. 31(2011), pp.914-946.

DOI: 10.1093/imanum/drp055

Google Scholar

[7] L. Cao, L. Zhang, W. Allegretto and Y. P. Lin, Multiscale asymptotic method for Steklov eigenvalue equations in composite media, SIAM J. Numer. Anal., Vol. 51(2013), pp.273-296.

DOI: 10.1137/110850876

Google Scholar

[8] M. G. Armentano, C. Padra and R. Rodrguezc, An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations, Comput. Methods Appl. Mech. Engrg., Vol. 200 (2011), pp.178-188.

DOI: 10.1016/j.cma.2010.08.003

Google Scholar

[9] H. Bi and Y. D. Yang, A two-grid method of the non-conforming Crouzeix-Raviart element for the Steklov eighvalue promblem, Appl. Math. Comp., Vol. 217(2011), pp.9669-9678.

DOI: 10.1016/j.amc.2011.04.051

Google Scholar

[10] C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, Spectral Methods Evolution to Complex Geometries and Applications to Fluid Dynamics, Springer (2007).

DOI: 10.1007/978-3-540-30728-0

Google Scholar

[11] J. Shen, T. Tang and L. Wang, Spectral Methods Algorithms, Analysis and Applications, Springer, Heidelberg (2011), pp.367-410.

Google Scholar

[12] I. Babuska and J. Osborm, Eigenvalue Problems, in: P. G. Ciarlet, J. L. Lions, (Ed. ), Finite El-ement Methods (Part 1), Handbook of Numerical Analysis, vol. 2, Elsevier Science Publishers, North-Holand (1991), pp.640-787.

Google Scholar

[13] P. Grisvard, Elliptic Problems for Non-smooth Domains, SIAM, Philadelphia (2011).

Google Scholar

[14] Y. D. Yang, Finite Element Methods for Eigenvalue Problems (in Chinese), Science Press, Beijing (2012).

Google Scholar