Lower spectral bounds by Wilson's brick discretization

DOI10.1016/j.apnum.2010.03.019zbMath1198.65220OpenAlexW2073385339MaRDI QIDQ979219

Hai Bi, Yidu Yang

Publication date: 25 June 2010

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2010.03.019

zbMATH Keywords

eigenvalue problemLaplace operatorspectral boundWilson element

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

Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations., Upper spectral bounds and a posteriori error analysis of several mixed finite element approximations for the Stokes eigenvalue problem, Computing the lower and upper bounds of Laplace eigenvalue problem by combining conforming and nonconforming finite element methods, The correction operator for the canonical interpolation operator of the Adini element and the lower bounds of eigenvalues, The extrapolation of numerical eigenvalues by finite elements for differential operators, Lower bounds for eigenvalues of elliptic operators: by nonconforming finite element methods, An extended family of nonconforming quasi-Wilson elements for solving elasticity problem, Lower and upper bounds of Stokes eigenvalue problem based on stabilized finite element methods, A posterior error estimator and lower bound of a nonconforming finite element method

Cites Work

• The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators
• New expansions of numerical eigenvalues by Wilson's element
• A convergence condition for the quadrilateral Wilson element
• Convergence of the nonconforming Wilson element for arbitrary quadrilateral meshes
• Superconvergence analysis and error expansion for the Wilson nonconforming finite element
• A new superconvergence property of Wilson nonconforming finite element
• Asymptotic lower bounds for eigenvalues by nonconforming finite element methods
• Wilson's element for the Reissner-Mindlin plate
• Nonconforming finite element approximations of the Steklov eigenvalue problem
• Eigenvalue approximation from below using non-conforming finite elements
• New expansions of numerical eigenvalues for $-\Delta u=\lambda \rho u$ by nonconforming elements
• Analysis of Some Quadrilateral Nonconforming Elements for Incompressible Elasticity
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