Generalized Rayleigh quotient and finite element two-grid discretization schemes

DOI10.1007/s11425-009-0016-8zbMath1188.65151OpenAlexW2047742486MaRDI QIDQ1044266

Xinyue Fan, Yidu Yang

Publication date: 11 December 2009

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-009-0016-8

zbMATH Keywords

finite elementstwo-grid discretization schemegeneralized Rayleigh quotientnonselfadjoint 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)

Related Items (11)

Convergence of some finite element iterative methods related to different Reynolds numbers for the 2D/3D stationary incompressible magnetohydrodynamics ⋮ Investigations on two kinds of two-grid mixed finite element methods for the elliptic eigenvalue problem ⋮ A two-scale discretization scheme for mixed variational formulation of eigenvalue problems ⋮ A note on the residual type a posteriori error estimates for finite element eigenpairs of nonsymmetric elliptic eigenvalue problems ⋮ Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem. ⋮ An efficient algorithm with stabilized finite element method for the Stokes eigenvalue problem ⋮ The local superconvergence of the linear finite element method for the poisson problem ⋮ A two-grid discretization scheme for the Steklov eigenvalue problem ⋮ A two-grid method of the non-conforming Crouzeix-Raviart element for the Steklov eigenvalue problem ⋮ A class of spectral element methods and its a priori/a posteriori error estimates for 2nd-order elliptic eigenvalue problems ⋮ Two-level quadratic equal-order stabilized method for the Stokes eigenvalue problem

Cites Work

• The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators
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• Asymptotic expansions and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for second order elliptic equations in perforated domains
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• Spectral analysis and numerical simulation for second order elliptic operator with highly oscillating coefficients in perforated domains with a periodic structure
• Iterated Galerkin Method for Eigenvalue Problems
• A two-grid discretization scheme for eigenvalue problems
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• Enhancing Eigenvalue Approximation by Gradient Recovery
• A Defect Correction Scheme for Finite Element Eigenvalues with Applications to Quantum Chemistry
• Semidefinite and second-order cone optimization approach for the Toeplitz matrix approximation problem
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