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

Hai Bi, Yidu Yang, Yuanyuan Yu & Jiayu Han

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

Published online: 2018-06

Preview Full PDF 6 1113
Export citation
  • 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)

  • References
  • Hide All
    View All

@Article{JCM-36-682, author = {Bi , Hai and Yang , Yidu and Yu , Yuanyuan and Han , Jiayu }, title = {New Error Estimates of Linear Triangle Finite Elements for 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} }
Copy to clipboard
The citation has been copied to your clipboard