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Volume 36, Issue 5
New Error Estimates for Linear Triangle Finite Elements in the Steklov Eigenvalue Problem

Hai Bi, Yidu Yang, Yuanyuan Yu & Jiayu Han

DOI: 10.4208/jcm.1703-m2014-0188

J. Comp. Math., 36 (2018), pp. 682-692.

Published online: 2018-06

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  • Abstract

This paper is concerned with the finite elements approximation for the Steklov eigenvalue problem on concave polygonal domain. We make full use of the regularity estimate and the characteristic of edge average interpolation operator of nonconforming Crouzeix-Raviart element, and prove a new and optimal error estimate in $‖·‖_{0,∂Ω}$ for the eigenfunction of linear conforming finite element and the nonconforming Crouzeix-Raviart element. Finally, we present some numerical results to support the theoretical analysis.

  • Keywords

Steklov eigenvalue problem, Concave polygonal domain, Linear conforming finite element, Nonconforming Crouzeix-Raviart element, Error estimates.

  • AMS Subject Headings

65N25, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

bihaimath@gznu.edu.cn (Hai Bi)

ydyang@gznu.edu.cn (Yidu Yang)

yuyuanyuan567@126.com (Yuanyuan Yu)

hanjiayu126@126.com (Jiayu Han)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-682, author = {Bi , HaiYang , YiduYu , Yuanyuan and Han , Jiayu}, title = {New Error Estimates for Linear Triangle Finite Elements in the Steklov Eigenvalue Problem}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {5}, pages = {682--692}, abstract = {

This paper is concerned with the finite elements approximation for the Steklov eigenvalue problem on concave polygonal domain. We make full use of the regularity estimate and the characteristic of edge average interpolation operator of nonconforming Crouzeix-Raviart element, and prove a new and optimal error estimate in $‖·‖_{0,∂Ω}$ for the eigenfunction of linear conforming finite element and the nonconforming Crouzeix-Raviart element. Finally, we present some numerical results to support the theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1703-m2014-0188}, url = {http://global-sci.org/intro/article_detail/jcm/12452.html} }
TY - JOUR T1 - New Error Estimates for Linear Triangle Finite Elements in the Steklov Eigenvalue Problem AU - Bi , Hai AU - Yang , Yidu AU - Yu , Yuanyuan AU - Han , Jiayu JO - Journal of Computational Mathematics VL - 5 SP - 682 EP - 692 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1703-m2014-0188 UR - https://global-sci.org/intro/article_detail/jcm/12452.html KW - Steklov eigenvalue problem, Concave polygonal domain, Linear conforming finite element, Nonconforming Crouzeix-Raviart element, Error estimates. AB -

This paper is concerned with the finite elements approximation for the Steklov eigenvalue problem on concave polygonal domain. We make full use of the regularity estimate and the characteristic of edge average interpolation operator of nonconforming Crouzeix-Raviart element, and prove a new and optimal error estimate in $‖·‖_{0,∂Ω}$ for the eigenfunction of linear conforming finite element and the nonconforming Crouzeix-Raviart element. Finally, we present some numerical results to support the theoretical analysis.

Hai Bi, Yidu Yang, Yuanyuan Yu & Jiayu Han. (2020). New Error Estimates for Linear Triangle Finite Elements in the Steklov Eigenvalue Problem. Journal of Computational Mathematics. 36 (5). 682-692. doi:10.4208/jcm.1703-m2014-0188
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