Postprocessing and higher order convergence of the mixed finite element approximations of biharmonic eigenvalue problems

DOI10.1016/j.cam.2004.12.015zbMath1075.65136OpenAlexW2095944824MaRDI QIDQ557771

Andrey Andreev, Raytcho D. Lazarov, Milena Racheva

Publication date: 30 June 2005

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.12.015

zbMATH Keywords

convergenceerror estimatesnumerical examplesmultigrid methodmixed finite element methodpostprocessingbiharmonic eigenvalue problem

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) 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 (26)

A C⁰ virtual element method for the biharmonic eigenvalue problem ⋮ FE-holomorphic operator function method for nonlinear plate vibrations with elastically added masses ⋮ A multi-level mixed element method for the eigenvalue problem of biharmonic equation ⋮ The two-grid and multigrid discretizations of the \(C^0\)IPG method for biharmonic eigenvalue problem ⋮ On gradient-type optimization method utilizing mixed finite element approximation for optimal boundary control problem governed by bi-harmonic equation ⋮ A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering ⋮ Postprocessing and higher order convergence for the mixed finite element approximations of the eigenvalue problem ⋮ Acceleration of stabilized finite element discretizations for the Stokes eigenvalue problem ⋮ An hp-mixed discontinuous Galerkin method for the biharmonic eigenvalue problem ⋮ A type of multi-level correction scheme for eigenvalue problems by nonconforming finite element methods ⋮ A virtual element method for the vibration problem of Kirchhoff plates ⋮ A Zienkiewicz-type finite element applied to fourth-order problems ⋮ Two-sided bounds of eigenvalues of second- and fourth-order elliptic operators. ⋮ The two-grid discretization of Ciarlet-Raviart mixed method for biharmonic eigenvalue problems ⋮ The optimal order convergence for the lowest order mixed finite element method of the biharmonic eigenvalue problem ⋮ SoftFEM: revisiting the spectral finite element approximation of second-order elliptic operators ⋮ Optimal spectral approximation of \(2 n\)-order differential operators by mixed isogeometric analysis ⋮ Superconvergent two-grid methods for elliptic eigenvalue problems ⋮ An efficient algorithm with stabilized finite element method for the Stokes eigenvalue problem ⋮ A mixed Legendre-Galerkin spectral method for the buckling problem of simply supported Kirchhoff plates ⋮ Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems ⋮ A multilevel correction method for Stokes eigenvalue problems and its applications ⋮ A mixed finite element method for fourth order eigenvalue problems ⋮ A multi-level correction scheme for eigenvalue problems ⋮ A new family of mixed method for the biharmonic eigenvalue problem based on the first order equations of Hellan-Herrmann-Johnson type ⋮ A finite element method for the buckling problem of simply supported Kirchhoff plates

Cites Work

• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• A mixed finite element method for the biharmonic eigenvalue problems of plate bending
• Nonconforming finite element methods for eigenvalue problems in linear plate theory
• On the mixed finite element approximation for the buckling of plates
• ON SIGN VARIATION AND THE ABSENCE OF "STRONG" ZEROS OF SOLUTIONS OF ELLIPTIC EQUATIONS
• Eigenvalue approximations by mixed methods
• On the boundary value problem of the biharmonic operator on domains with angular corners
• A hybrid finite element method to compute the free vibration frequencies of a clamped plate
• Eigenvalue Approximation by Mixed and Hybrid Methods
• Mixed and Hybrid Finite Element Methods
• L ^p Spectral Theory of Higher-Order Elliptic Differential Operators
• A two-grid discretization scheme for eigenvalue problems
• Superconvergence Postprocessing for Eigenvalues
• Equivalent Norms for Sobolev Spaces
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