Asymptotic error expansion and Richardson extrapolation of eigenvalue approximations for second order elliptic problems by the mixed finite element method

DOI10.1016/j.apnum.2009.01.011zbMath1201.65202OpenAlexW2058400338WikidataQ112880212 ScholiaQ112880212MaRDI QIDQ1030672

Qun Lin, Hehu Xie

Publication date: 2 July 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2009.01.011

zbMATH Keywords

mixed finite element methodRichardson extrapolationasymptotic error expansionRaviart-Thomas elementsecond order elliptic eigenvalue problem

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Acceleration of convergence in numerical analysis (65B99)

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Cites Work

• Fourth order eigenvalue approximation by extrapolation on domains with reentrant corners
• Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method.
• Superconvergence and a posteriori error estimation for triangular mixed finite elements
• Global Estimates for Mixed Methods for Second Order Elliptic Equations
• New expansions of numerical eigenvalues for $-\Delta u=\lambda \rho u$ by nonconforming elements
• Asymptotic Expansions and Richardson Extrapolation of Approximate Solutions for Second Order Elliptic Problems on Rectangular Domains by Mixed Finite Element Methods
• Estimates for the Errors in Eigenvalue and Eigenvector Approximation by Galerkin Methods, with Particular Attention to the Case of Multiple Eigenvalues
• Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfadjoint Problems
• Mixed and Hybrid Finite Element Methods
• A two-grid discretization scheme for eigenvalue problems
• Eigenvalue approximation of the biharmonic eigenvalue problem by Ciarlet-Raviart scheme
• A POSTERIORI ERROR ESTIMATORS FOR MIXED APPROXIMATIONS OF EIGENVALUE PROBLEMS
• The Splitting Extrapolation Method
• Finite Element Methods and Their Applications
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