A posteriori error analysis of nonconforming methods for the eigenvalue problem

DOI10.1007/s11424-009-9181-7zbMath1188.65150OpenAlexW2171431388MaRDI QIDQ967999

Youai Li

Publication date: 3 May 2010

Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11424-009-9181-7

zbMATH Keywords

Laplace equationa posteriori error analysisStokes equationnonconforming finite elementlinear elasticity problemssecond order elliptic eigenvalue problem

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

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Cites Work

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• A posteriori error estimates for nonconforming finite element methods
• A unifying theory of a posteriori error control for nonconforming finite element methods
• A unifying theory of a posteriori finite element error control
• A Posteriori Error Estimates for the Finite Element Approximation of Eigenvalue Problems
• Robust a posteriori error estimation for the nonconforming Fortin--Soulie finite element approximation
• Simple nonconforming quadrilateral Stokes element
• A Local Regularization Operator for Triangular and Quadrilateral Finite Elements
• P₁-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems
• A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems
• Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation
• Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
• A posteriori error estimators for nonconforming finite element methods
• Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
• Framework for the A Posteriori Error Analysis of Nonconforming Finite Elements