Eigenvalue approximation by the finite element method: the method of Lagrange multipliers

Author:
William G. Kolata

Journal:
Math. Comp. **33** (1979), 63-76

MSC:
Primary 65N25; Secondary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1979-0514810-0

MathSciNet review:
514810

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Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to investigate the application of the finite element method of Lagrange multipliers to the problem of approximating the eigenvalues of a selfadjoint elliptic operator satisfying Dirichlet boundary conditions. Although the Lagrange multiplier method is not a Rayleigh-Ritz-Galerkin approximation scheme, it is shown that at least asymptotically the Lagrange multiplier method has some of the properties of such a scheme. In particular, the approximate eigenvalues are greater than or equal to the exact eigenvalues and can be computed from a nonnegative definite matrix problem. It is also shown that the known estimates for the eigenvalue error are optimal.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0514810-0

Keywords:
Finite element method,
Lagrange multipliers,
selfadjoint elliptic eigenvalue problems

Article copyright:
© Copyright 1979
American Mathematical Society