Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations

Qin Li; Qun Lin; Hehu Xie

Applications of Mathematics (2013)

  • Volume: 58, Issue: 2, page 129-151
  • ISSN: 0862-7940

Abstract

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The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, Q 1 rot , E Q 1 rot and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to validate our theoretical results.

How to cite

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Li, Qin, Lin, Qun, and Xie, Hehu. "Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations." Applications of Mathematics 58.2 (2013): 129-151. <http://eudml.org/doc/252552>.

@article{Li2013,
abstract = {The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, $Q_\{1\}^\{\rm rot\}$, $EQ_\{1\}^\{\rm rot\}$ and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to validate our theoretical results.},
author = {Li, Qin, Lin, Qun, Xie, Hehu},
journal = {Applications of Mathematics},
keywords = {Steklov eigenvalue problem; nonconforming finite element; error estimate; lower bound of the eigenvalues; Steklov eigenvalue problem; nonconforming finite element; error estimate; numerical examples; lower bound approximations; second-order elliptic equation; convergence; eigenfunctions},
language = {eng},
number = {2},
pages = {129-151},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations},
url = {http://eudml.org/doc/252552},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Li, Qin
AU - Lin, Qun
AU - Xie, Hehu
TI - Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 129
EP - 151
AB - The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, $Q_{1}^{\rm rot}$, $EQ_{1}^{\rm rot}$ and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to validate our theoretical results.
LA - eng
KW - Steklov eigenvalue problem; nonconforming finite element; error estimate; lower bound of the eigenvalues; Steklov eigenvalue problem; nonconforming finite element; error estimate; numerical examples; lower bound approximations; second-order elliptic equation; convergence; eigenfunctions
UR - http://eudml.org/doc/252552
ER -

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