Approximation of the Spectrum of Closed Operators: The Determination of Normal Modes of a Rotating Basin

DOI10.2307/2007731zbMath0458.65084OpenAlexW4250264051MaRDI QIDQ3908436

Mitchell Luskin, Jacques Rappaz, Jean Descloux

Publication date: 1981

Full work available at URL: https://doi.org/10.2307/2007731

zbMATH Keywords

finite element methodshallow water equationsspectral approximationclosed operatorsoptimal order estimates

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Spectrum, resolvent (47A10) General theory of partial differential operators (47F05) Numerical solutions to equations with linear operators (65J10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing (76B10)

Related Items (9)

Convergence of a Finite Element Method for the Approximation of Normal Modes of the Oceans ⋮ Constructive spectral approaches for the Helmholtz decomposition of a vector field ⋮ A new \(hp\) method for the \(-\mathrm{grad}(\mathrm{div})\) operator in non-Cartesian geometries ⋮ High performance computing for partial differential equations ⋮ Error bounds for an isolated eigenvalue obtained by the Galerkin method ⋮ Legendre spectral methods for the - grad(div) operator ⋮ Approximation of solution branches of nonlinear equations ⋮ Galerkin eigenvector approximations ⋮ Finite elements for the eigenvalue problem of differential operators in unbounded intervals

Cites Work

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• Perturbation theory for nullity, deficiency and other quantities of linear operators
• Error bounds for an isolated eigenvalue obtained by the Galerkin method
• Local boundary conditions for dissipative symmetric linear differential operators
• The Resolvent Stability Condition for Spectra Convergence with Application to the Finite Element Approximation of Noncompact Operators
• Optimal Error Estimates for the Finite Element Spectral Approximation of Noncompact Operators
• Convergence of a Finite Element Method for the Approximation of Normal Modes of the Oceans
• Rate of Convergence Estimates for Nonselfadjoint Eigenvalue Approximations
• Spectral Approximation for Compact Operators
• On spectral approximation. Part 1. The problem of convergence

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