A posteriori error estimates with computable upper bound for the nonconforming rotated \(Q_1\) finite element approximation of the eigenvalue problems
type: Item
instance of: scholarly article
title: A posteriori error estimates with computable upper bound for the nonconforming rotated \(Q_1\) finite element approximation of the eigenvalue problems
zbMATH Open document ID: 1407.65273
DOI: 10.1155/2014/891278
author: Xianqiang Yang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper discusses the nonconforming rotated \(Q_1\) finite element computable upper bound a posteriori error estimate of the boundary value problem established by M. Ainsworth and obtains efficient computable upper bound a posteriori error indicators for the eigenvalue problem associated with the boundary value problem. We extend the a posteriori error estimate to the Steklov eigenvalue problem and also derive efficient computable upper bound a posteriori error indicators. Finally, through numerical experiments, we verify the validity of the a posteriori error estimate of the boundary value problem; meanwhile, the numerical results show that the a posteriori error indicators of the eigenvalue problem and the Steklov eigenvalue problem are effective.
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35P15
zbMATH DE Number: 7017518
Wikidata QID: Q59070405
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/891278
OpenAlex ID: W2046943742
cites work: A‐posteriori error estimates for the finite element method
cites work: Q4680699
cites work: Framework for the A Posteriori Error Analysis of Nonconforming Finite Elements
cites work: 特征值问题协调/非协调有限元后验误差分析
cites work: A class of spectral element methods and its a priori/a posteriori error estimates for 2nd-order elliptic eigenvalue problems
cites work: Isoparametric finite-element approximation of a Steklov eigenvalue problem
cites work: The effect of reduced integration in the Steklov eigenvalue problem
cites work: Q5680514
cites work: Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations.
cites work: Nonconforming finite element approximations of the Steklov eigenvalue problem
cites work: A posteriori error estimates for the Steklov eigenvalue problem
cites work: Local a priori/a posteriori error estimates of conforming finite elements approximation for Steklov eigenvalue problems
cites work: Spectral method with the tensor-product nodal basis for the Steklov eigenvalue problem
cites work: Simple nonconforming quadrilateral Stokes element
cites work: Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
cites work: Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation
cites work: Eigenvalue approximation from below using non-conforming finite elements
cites work: Asymptotic lower bounds for eigenvalues by nonconforming finite element methods
description: scientific article; zbMATH DE number 7017518